Messages from 2012
These are the messages distributed to the Banach list during 2012.
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Grzegorz Plebanek and Jose
Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:44:03 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A weak* separable C(K)* space
whose unit ball is not weak* separable" by Antonio Aviles, Grzegorz
Plebanek and Jose Rodriguez.
Abstract: We provide a ZFC example of a compact space K such that C(K)* is
w*-separable but its closed unit ball is not w*-separable. All previous
examples of such kind had been constructed under CH. We also discuss
the measurability of the supremum norm on that C(K) equipped with its
weak Baire sigma-algebra.
Archive classification: math.FA math.GN
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.5710
or
http://arXiv.org/abs/1112.5710
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by M. Jimenez-Sevilla and L. Sanchez-Gonzalez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:45:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On smooth extensions of
vector-valued functions defined on closed subsets of Banach spaces"
by M. Jimenez-Sevilla and L. Sanchez-Gonzalez.
Abstract: Let $X$ and $Z$ be Banach spaces, $A$ a closed subset of $X$
and a mapping $f:A \to Z$. We give necessary and sufficient conditions
to obtain a $C^1$ smooth mapping $F:X \to Z$ such that $F_{\mid_A}=f$,
when either (i) $X$ and $Z$ are Hilbert spaces and $X$ is separable,
or (ii) $X^*$ is separable and $Z$ is an absolute Lipschitz retract,
or (iii) $X=L_2$ and $Z=L_p$ with $1<p<2$, or (iv) $X=L_p$ and $Z=L_2$
with $2<p<\infty$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 17 pages
Submitted from: lfsanche at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.5888
or
http://arXiv.org/abs/1112.5888
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino, Joedson Santos and Juan
B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:47:49 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A general Extraplolation Theorem
for absolutely summing operators" by Daniel Pellegrino, Joedson Santos
and Juan B. Seoane-Sepulveda.
Abstract: In this note we prove a general version of the Extrapolation
Theorem, extending the classical linear extrapolation theorem due to
B. Maurey. Our result shows, in particular, that the operators involved
do not need to be linear.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.5901
or
http://arXiv.org/abs/1112.5901
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Taras Banakh, Ivan Hetman, and Katsuro
Sakai
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:51:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Recognizing the topology of the
space of closed convex subsets of a Banach space" by Taras Banakh,
Ivan Hetman, and Katsuro Sakai.
Abstract: Let $X$ be a Banach space and $Conv_H(X)$ be the space of
non-empty closed convex subsets of $X$, endowed with the Hausdorff metric
$d_H$. We prove that each connected component of the space $Conv_H(X)$ is
homeomorphic to one of the spaces: a singleton, the real line, a closed
half-plane, the Hilbert cube multiplied by the half-line, the separable
Hilbert space, or a Hilbert space of density not less than continuum.
Archive classification: math.GT math.FA math.GN math.OC
Mathematics Subject Classification: 57N20, 46A55, 46B26, 46B20, 52B05,
03E65
Remarks: 10 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.6374
or
http://arXiv.org/abs/1112.6374
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:53:45 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on the combinatorial
generation of Musielak-Orlicz spaces" by Joscha Prochno.
Abstract: We show, how one can generate Musielak-Orlicz norms, using
matrix averages and combinatorial inequalities.
Archive classification: math.FA
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0108
or
http://arXiv.org/abs/1201.0108
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Koldobsky, G. Paouris and M.
Zymonopoulou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:55:27 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Complex intersection bodies"
by A. Koldobsky, G. Paouris and M. Zymonopoulou.
Abstract: We introduce complex intersection bodies and show that
their properties and applications are similar to those of their real
counterparts. In particular, we generalize Busemann's theorem to the
complex case by proving that complex intersection bodies of symmetric
complex convex bodies are also convex. Other results include stability
in the complex Busemann-Petty problem for arbitrary measures and the
corresponding hyperplane inequality for measures of complex intersection
bodies.
Archive classification: math.FA
Submitted from: marisa.zym at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0437
or
http://arXiv.org/abs/1201.0437
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pascal Lefevre, Daniel Li, Herve Queffelec,
and Luis Rodriguez-Piazza
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:58:41 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some new properties of composition
operators associated with lens maps" by Pascal Lefevre, Daniel Li,
Herve Queffelec, and Luis Rodriguez-Piazza.
Abstract: We give examples of results on composition operators connected
with lens maps. The first two concern the approximation numbers of
those operators acting on the usual Hardy space $H^2$. The last ones
are connected with Hardy-Orlicz and Bergman-Orlicz spaces $H^\psi$ and
$B^\psi$, and provide a negative answer to the question of knowing if
all composition operators which are weakly compact on a non-reflexive
space are norm-compact.
Archive classification: math.FA
Remarks: 21 pages
Submitted from: daniel.li at euler.univ-artois.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0636
or
http://arXiv.org/abs/1201.0636
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas P. Hytonen and Antti V. Vahakangas
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 12:00:15 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The local non-homogeneous Tb
theorem for vector-valued functions" by Tuomas P. Hytonen and Antti
V. Vahakangas.
Abstract: We extend the local non-homogeneous Tb theorem of Nazarov, Treil
and Volberg to the setting of singular integrals with operator-valued
kernel that act on vector-valued functions. Here, `vector-valued'
means `taking values in a function lattice with the UMD (unconditional
martingale differences) property'. A similar extension (but for general
UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global
non-homogeneous Tb theorem was achieved earlier by the first author,
and it has found applications in the work of Mayboroda and Volberg on
square-functions and rectifiability. Our local version requires several
elaborations of the previous techniques, and raises new questions about
the limits of the vector-valued theory.
Archive classification: math.FA
Mathematics Subject Classification: 42B20 (Primary), 42B25, 46E40, 60G46
(Secondary)
Submitted from: antti.vahakangas at helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0648
or
http://arXiv.org/abs/1201.0648
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Godefroy and Narutaka Ozawa
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 12:01:35 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Free Banach spaces and the
approximation properties" by Gilles Godefroy and Narutaka Ozawa.
Abstract: We characterize the metric spaces whose free space has the
bounded approximation property through a Lipschitz analogue of the local
reflexivity principle. We show that there exist compact metric spaces
whose free spaces fail the approximation property.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B28, 46B50
Remarks: 7 pages
Submitted from: narutaka at kurims.kyoto-u.ac.jp
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0847
or
http://arXiv.org/abs/1201.0847
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Postdoctoral Fellowship in BESANCON, France
From: "Stanislaw J. Szarek" <szarek at cwru.edu>
Date: Thu, 2 Feb 2012 13:43:59 -0500 (12:43 CST)
To: banach at math.okstate.edu
Title: Postdoctoral Research Fellowship in Functional Analysis in
Besançon, France
Period: September 1, 2012 to August 31, 2013
Deadline for application: May 1, 2012.
We are now accepting applications for a postdoctoral research
fellowship (without teaching duty) for the academic year 2012-2013
(starting date: Sept. 1,2012) in the framework of the ANR project
OSQPI (Interactions between Operator Space Theory and Quantum
Probability with Applications to Quantum Information). We are looking
for applicants who received their Ph.D. recently (or will receive it
until August 2012). The fellow is expected to carry out a research
project on the topics of the ANR project OSQPI (operator spaces,
noncommutative Lp spaces, noncommutative harmonic analysis, quantum
probability, and their applications in quantum information) at the
Laboratoire de Mathématiques de Besançon (Université de
Franche-Comté). Part of the program could also be carried out at
partner institutions in Paris, Lyon, or Toulouse. The fellowship
provides a salary of about 1.800 euro per month after taxes.
For more details please contact quanhua.xu at univ-fcomte.fr
Applications should be sent to quanhua.xu at univ-fcomte.fr
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
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Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:26:57 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Absolute sums of Banach spaces
and some geometric properties related to rotundity and smoothness"
by Jan-David Hardtke.
Abstract: We study the notions of acs, luacs and uacs Banach spaces
which were introduced by V. Kadets et al. in 2000 and form common
generalisations of the usual rotundity and smoothness properties of
Banach spaces. In particular, we are interested in (mainly infinite)
absolute sums of such spaces. We also introduce some new classes of
spaces that lie inbetween those of acs and uacs spaces and study their
behaviour under taking absolute sums as well.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 42 pages, 8 figures
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.2300
or
http://arXiv.org/abs/1201.2300
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gareth Speight
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:31:46 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Surfaces meeting porous sets in
positive measure" by Gareth Speight.
Abstract: Let n>2 and X be a Banach space of dimension strictly greater
than n. We show there exists a directionally porous set P in X for which
the set of C^1 surfaces of dimension n meeting P in positive measure is
not meager. If X is separable this leads to a decomposition of X into
a countable union of directionally porous sets and a set which is null
on residually many C^1 surfaces of dimension n. This is of interest
in the study of certain classes of null sets used to investigate
differentiability of Lipschitz functions on Banach spaces.
Archive classification: math.FA math.CA math.MG
Mathematics Subject Classification: 28A75, 46T99, 46G99
Submitted from: G.Speight at Warwick.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.2376
or
http://arXiv.org/abs/1201.2376
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino and Juan B.
Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:33:41 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the hypercontractivity of the
polynomial Bohnenblust--Hille inequality" by Daniel Pellegrino and Juan
B. Seoane-Sepulveda.
Abstract: Recently, it was proved that the polynomial Bohnenblust--Hille
inequality is hypercontractive, i.e., there is a constant $C>1$
(from now on called constant of hypercontractivity) so that
$\frac{D_{m}}{D_{m-1}}=C$ for every $m$, where $D_{m}$ are constants
satisfying the polynomial Bohnenblust--Hille inequality. For the
case of multilinear mappings a recent result shows that $\lim
_{m\rightarrow\infty}\frac{C_{m}}{C_{m-1}}=1$, where $C_{m}$ are
constants satisfying the multilinear Bohnenblust--Hille inequality. So
it is natural to wonder if there exist constants $D_{m}$'s such that
$\lim_{m\rightarrow\infty}\frac{D_{m}% }{D_{m-1}}=1$. In this note we
provide lower estimates for the polynomial Bohnenblust--Hille inequality
with strong numerical evidence supporting that it is not possible to
obtain such $D_{m}.$ Besides the qualitative information, and to the
best of our knowledge, this is the first time in which non-trivial lower
bounds for the constants of the polynomial Bohnenblust--Hille inequality
are presented. We also show that the constant of hypercontractivity $C$
is so that $1.1542\leq C\leq1.8529$, providing as well explicit formulae
to improve the lower estimate $1.1542.$ It is our belief that variations
of the ideas introduced in this paper can be used for the search of the
optimal constants for the polynomial Bohnenblust--Hille inequality.
Archive classification: math.FA
Remarks: 2 figures
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.3873
or
http://arXiv.org/abs/1201.3873
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by V. Mykhaylyuk, M. Popov and B.
Randrianantoanina
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:37:27 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Enflo and narrow operators
acting on $L_p$" by V. Mykhaylyuk, M. Popov and B. Randrianantoanina.
Abstract: The paper is devoted to proofs of the following three
results. Theorem A. For $1 < p < 2$ every non-Enflo operator $T$ on $L_p$
is narrow. Theorem B. For $1 < p < 2$ every operator $T$ on $L_p$ which
is unbounded from below on $L_p(A)$, $A \subseteq [0,1]$, by means of
function having a ``gentle'' growth, is narrow. Theorem C. For $2 < p,
r < \infty$ every operator $T: L_p\rightarrow\ell_r$ is narrow.
Theorem A was mentioned by Bourgain in 1981, as a result that can
be deduced from the proof of a related result in
Johnson-Maurey-Schechtman-Tzafriri's book, but the proof from there
needed several modifications. Theorems B and C are new results. We also
discuss related open problems.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B07, secondary 47B38, 46B03
Submitted from: randrib at muohio.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.4041
or
http://arXiv.org/abs/1201.4041
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuele Casini, Enrico Miglierina, Ioannis
A. Polyrakis, and Foivos Xanthos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:44:21 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Reflexive Cones" by Emanuele
Casini, Enrico Miglierina, Ioannis A. Polyrakis, and Foivos Xanthos.
Abstract: Reflexive cones in Banach spaces are cones with weakly compact
intersection with the unit ball. In this paper we study the structure of
this class of cones. We investigate the relations between the notion of
reflexive cones and the properties of their bases. This allows us to prove
a characterization of reflexive cones in term of the absence of a subcone
isomorphic to the positive cone of \ell_{1}. Moreover, the properties
of some specific classes of reflexive cones are investigated. Namely,
we consider the reflexive cones such that the intersection with the
unit ball is norm compact, those generated by a Schauder basis and the
reflexive cones regarded as ordering cones in a Banach spaces. Finally,
it is worth to point out that a characterization of reflexive spaces and
also of the Schur spaces by the properties of reflexive cones is given.
Archive classification: math.FA
Mathematics Subject Classification: 46B10, 46B20, 46B40, 46B42
Remarks: 23 pages
Submitted from: enrico.miglierina at unicatt.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.4927
or
http://arXiv.org/abs/1201.4927
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Greg Knese
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:46:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uchiyama's lemma and the
John-Nirenberg inequality" by Greg Knese.
Abstract: Using integral formulas based on Green's theorem and in
particular a lemma of Uchiyama, we give simple proofs of comparisons of
different BMO norms without using the John-Nirenberg inequality while we
also give a simple proof of the strong John-Nirenberg inequality. Along
the way we prove the inclusions of BMOA in the dual of H^1 and BMO in
the dual of real H^1.
Archive classification: math.CV math.FA
Mathematics Subject Classification: 30H35, 30H10, 30J99
Remarks: 13 pages
Submitted from: geknese at bama.ua.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.5354
or
http://arXiv.org/abs/1201.5354
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hermann Pfitzner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:48:46 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A conjecture of Godefroy concerning
James' theorem" by Hermann Pfitzner.
Abstract: In this note we look at the interdependences between James'
theorem and the boundary problem. To do so we show a variant of James'
sup-theorem for C(K)-spaces conjectured by Godefroy: in order to know
that a bounded weakly closed subset of a C(K)- space is weakly compact
it is enough to test the sup-attainment only for measures with countable
support.
Archive classification: math.FA
Remarks: to appear in Quarterly Journal of Math.
Submitted from: Hermann.Pfitzner at univ-orleans.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.5471
or
http://arXiv.org/abs/1201.5471
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sebastian Scholtes
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:51:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A characterisation of inner product
spaces by the maximal circumradius of spheres" by Sebastian Scholtes.
Abstract: We will give a new characterisation of inner product spaces
amongst normed vector spaces in terms of the maximal cirumradius of
spheres. It will turn out that a normed vector space $(X,\norm{\cdot})$
with $\dim X\geq 2$ is an inner product space if and only if all spheres
are not degenerate, i.e. the maximal circumradius of points on the sphere
equals their radius.
Archive classification: math.FA math.CA math.MG
Mathematics Subject Classification: 46C15, 46B20
Remarks: 8 pages
Submitted from: sebastian.scholtes at rwth-aachen.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.0503
or
http://arXiv.org/abs/1202.0503
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by William B. Johnson, Naratuka Ozawa, and
Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:52:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A quantitative version of the
commutator theorem for zero trace matrices" by William B. Johnson,
Naratuka Ozawa, and Gideon Schechtman.
Abstract: Let $A$ be a $m\times m$ complex matrix with zero trace and
let $\e>0$. Then there are $m\times m$ matrices $B$ and $C$ such that
$A=[B,C]$ and $\|B\|\|C\|\le K_\e m^\e\|A\|$ where $K_\e$ depends only
on $\e$. Moreover, the matrix $B$ can be taken to be normal.
Archive classification: math.FA
Mathematics Subject Classification: 47B47, 15A60
Submitted from: gideon at weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.0986
or
http://arXiv.org/abs/1202.0986
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Afonso S. Bandeira, Matthew Fickus, Dustin
G. Mixon and Percy Wong
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:54:33 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The road to deterministic matrices
with the restricted isometry property" by Afonso S. Bandeira, Matthew
Fickus, Dustin G. Mixon and Percy Wong.
Abstract: The restricted isometry property (RIP) is a well-known matrix
condition that provides state-of-the-art reconstruction guarantees
for compressed sensing. While random matrices are known to satisfy
this property with high probability, deterministic constructions have
found less success. In this paper, we consider various techniques for
demonstrating RIP deterministically, some popular and some novel, and
we evaluate their performance. In evaluating some techniques, we apply
random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class
of matrices as candidates for being RIP, namely, equiangular tight frames
(ETFs). Using the known correspondence between real ETFs and strongly
regular graphs, we investigate certain combinatorial implications of a
real ETF being RIP. Specifically, we give probabilistic intuition for
a new bound on the clique number of Paley graphs of prime order, and we
conjecture that the corresponding ETFs are RIP in a manner similar to
random matrices.
Archive classification: math.FA
Remarks: 23 pages
Submitted from: dmixon at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.1234
or
http://arXiv.org/abs/1202.1234
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kevin Beanland, Daniel Freeman, and Rui Liu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:58:13 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Upper and lower estimates for
Schauder frames and atomic decompositions" by Kevin Beanland, Daniel
Freeman, and Rui Liu.
Abstract: We prove that a Schauder frame for any separable Banach space
is shrinking if and only if it has an associated space with a shrinking
basis, and that a Schauder frame for any separable Banach space is
shrinking and boundedly complete if and only if it has a reflexive
associated space. To obtain these results, we prove that the upper and
lower estimate theorems for finite dimensional decompositions of Banach
spaces can be extended and modified to Schauder frames. We show as well
that if a separable infinite dimensional Banach space has a Schauder
frame, then it also has a Schauder frame which is not shrinking.
Archive classification: math.FA
Mathematics Subject Classification: 46B20 (Primary), 41A65 (Secondary)
Remarks: 22 pages
Submitted from: freeman at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.2492
or
http://arXiv.org/abs/1202.2492
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sean Li and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:59:29 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Discretization and affine
approximation in high dimensions" by Sean Li and Assaf Naor.
Abstract: Lower estimates are obtained for the macroscopic scale of
affine approximability of vector-valued Lipschitz functions on finite
dimensional normed spaces, completing the work of Bates, Johnson,
Lindenstrass, Preiss and Schechtman. This yields a new approach to
Bourgain's discretization theorem for superreflexive targets.
Archive classification: math.FA math.MG
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.2567
or
http://arXiv.org/abs/1202.2567
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cleon S. Barroso
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 14:01:14 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the minimal space problem and
a new result on existence of basic sequences in quasi-Banach spaces"
by Cleon S. Barroso.
Abstract: We prove that if $X$ is a quasi-normed space which possesses
an infinite countable dimensional subspace with a separating dual, then
it admits a strictly weaker Hausdorff vector topology. Such a topology
is constructed explicitly. As an immediate consequence, we obtain an
improvement of a well-known result of Kalton-Shapiro and Drewnowski by
showing that a quasi-Banach space contains a basic sequence if and only
if it contains an infinite countable dimensional subspace whose dual is
separating. We also use this result to highlight a new feature of the
minimal quasi-Banach space constructed by Kalton. Namely, which all of
its $\aleph_0$-dimensional subspaces fail to have a separating family
of continuous linear functionals.
Archive classification: math.FA
Submitted from: cleonbar at mat.ufc.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.3088
or
http://arXiv.org/abs/1202.3088
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Informal Analysis Seminar at Kent State
From: Artem Zvavitch <zvavitch at math.kent.edu>
Date: Tue, 28 Feb 2012 19:42:40 -0500 (18:42 CST)
To: banach at math.okstate.edu
Dear Friends,
On March 30-April 1, 2012, the Department of Mathematical Science at
Kent State University will host famous but still very informal: INFORMAL
ANALYSIS SEMINAR and Lecture Series in Ergodic Theory and Probability.
The plan for now is to start around 3pm Friday, and finish Sunday Evening
(around 5pm). We will have lecture series by
Yuval Peres (Microsoft Research) on "Transience of random walks,
Unpredictable paths, percolation and Kakeya sets".
Mark Rudelson (University of Michigan) on "Invertibility of random
matrices".
and lectures by
Pablo Galindo (Universidad de Valencia / Purdue University), TBA
Yun Sung Choi (Postech, Pohang South Korea) on "Slicely countably
determined Banach spaces"
Miguel Martin (University of Granada) on "The Uniform Convexity, Lushness
and Bishop-Phelps-Bollobas Property"
Please, also note that on Thursday, March 29 at 4:15pm we will have a
Colloquium talk by Sergei Treil (Brown University) at 4:15.
More information can be found on
http://www.kent.edu/math/events/conferences/informal-analysis-seminar-2012.cfm
The conference fee $65, which includes pick up/drop off from the
airport/hotel and Friday/Saturday/Sunday lunches/dinners to be provided at
the department. Also, a special price of $135 has been arranged for three
nights stay at the Microtel in Streetsboro OH. The reservation must be done
through the department. If you plan to stay fewer then 3 nights or prefer
to make your own accommodation arrangements please reduce your registration
fee by $45 for each day that you will not use our hotel. If possible,
please, send a check for your registration fee, made out to "The Department
of Mathematical Sciences" to Virginia Wright, The Department of
Mathematical Sciences, Kent, State University, Kent, OH, US, 44242. The fee
can be also paid during the registration (check/cash).
Depending on availability of funds, we may waive the registration fee for
young researchers and people without available funding!!!! Please contact
Artem Zvavitch (zvavitch at math.kent.edu) or Dmitry Ryabogin
(ryabogin at math.kent.edu) as soon as possible.
SORRY FOR THE SHORT NOTICE AND LOOKING FORWARD TO SEEING YOU IN KENT!
Very Informal Analysis Group At Kent State
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Workshop at A&M
Date: Tue, 13 Mar 2012 14:29:43 -0500 (CDT)
From: Bill Johnson <johnson at math.tamu.edu>
To: banach at math.okstate.edu
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2012
The Summer 2012 Workshop in Analysis and Probability at Texas A&M
University will be in session from July 2 until August 10, 2012. For
information about the Workshop, consult the Workshop Home Page, whose NEW
URL is
http://www.math.tamu.edu/~kerr/workshop/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held
August 3-5.
July 16 - 19 there will be a Concentration Week on "Frame Theory and Maps
Between Operator Algebras",
organized by Chris Heil, Emily J. King (chair), Keri Kornelson, David
Larson (local organizer), and Darrin Speegle. A researcher working in
frame theory will naturally be led to consider matrices (the Gram matrix,
the analysis operator and the synthesis operator), and many problems in
frame theory have a re-casting in operator theory. The most celebrated
example of this is the Kadison-Singer problem. By now, there are many
mathematicians familiar with the basics of the two areas, and there is a
fruitful collaboration. Less obvious is the relationship between frame
theory and maps between operator algebras. Very recent work in this area
by Han, Larson, Lu, and Lu indicate that this may be a relationship that
is ripe for exploiting. The goal of this concentration week is to bring
together researchers in these two fields so that they may learn from one
another and build networks of potential collaborators. There will be
introductory series of talks on "Frame theory" by Ole Christensen, on
"Maps on Operator Algebras" by Vern Paulsen, and on "Bridging the Gap
Between Frame Theory and Maps on Operator Algebras" by Deguang Han. This
concentration week will also lead into a separate conference on the
following weekend celebrating the 70th birthday of David Larson. The home
page for this Workshop is at
http://page.math.tu-berlin.de/~king/cw.html
August 6-10 there will be a Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory",
organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and
Alexei Poltoratski. This CW is designed to bring together two groups of
experts: those specializing in complex and harmonic analysis and those
working in spectral theory of differential operators and mathematical
physics. The main goals of the CW are to study new relationships and to
widen further participation in this area in the United States.
Introductory series of lectures by Stephen Gustafson, Svetlana
Jitomirskaya (to be confirmed), Helge Krueger, and Brett Wick are planned
to acquaint non-experts with these topics with the reasonable expectation
that some the participants in the larger Workshop will be attracted to
this program and inject new ideas into the area.
The home page for this Workshop is at
http://www.math.tamu.edu/~comech/events/hast-2012/
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Frame Theory and Maps
Between Operator Algebras" contact Emily King <eking at math.umd.edu>
For information about the Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory" contact Constanze Liaw
<conni at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pawel Wolff
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:37:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On randomness reduction in the
Johnson-Lindenstrauss lemma" by Pawel Wolff.
Abstract: A refinement of so-called fast Johnson-Lindenstrauss
transform, due to Ailon and Chazelle (2006), and Matou\v{s}ek (2008),
is proposed. While it preserves the time efficiency and simplicity
of implementation of the original construction, it reduces randomness
used to generate the random transformation. In the analysis of the
construction two auxiliary results are established which might be
of independent interest: a Bernstein-type inequality for a sum of a
random sample from a family of independent random variables and a normal
approximation result for such a sum.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60E15, 46B85
Submitted from: pawel.wolff at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.5500
or
http://arXiv.org/abs/1202.5500
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. A. Argyros, V. Kanellopoulos, and K.
Tyros
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:42:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Higher order spreading models"
by S. A. Argyros, V. Kanellopoulos, and K. Tyros.
Abstract: We introduce the higher order spreading models associated
to a Banach space $X$. Their definition is based on $\ff$-sequences
$(x_s)_{s\in\ff}$ with $\ff$ a regular thin family and the
plegma families. We show that the higher order spreading models
of a Banach space $X$ form an increasing transfinite hierarchy
$(\mathcal{SM}_\xi(X))_{\xi<\omega_1}$. Each $\mathcal{SM}_\xi
(X)$ contains all spreading models generated by $\ff$-sequences
$(x_s)_{s\in\ff}$ with order of $\ff$ equal to $\xi$. We also provide
a study of the fundamental properties of the hierarchy.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B03, 46B06, 46B25, 46B45,
Secondary 05D10
Remarks: 37 pages
Submitted from: chcost at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.6390
or
http://arXiv.org/abs/1202.6390
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonis Manoussakis and Anna
Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:44:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strictly singular non-compact
operators on a class of HI spaces" by Antonis Manoussakis and Anna
Pelczar-Barwacz.
Abstract: We present a method for constructing bounded strictly singular
non-compact operators on mixed Tsirelson spaces defined either by the
families (A_n) or (S_n) of a certain class, as well as on spaces built
on them, including hereditarily indecomposable spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B15
Remarks: 19 pages
Submitted from: anna.pelczar at im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.0243
or
http://arXiv.org/abs/1203.0243
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gianluca Cassese
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:52:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some implications of Lebesgue
decomposition" by Gianluca Cassese.
Abstract: Based on a generalization of Lebesgue decomposition we obtain a
characterization of weak compactness in the space $ba$, a representation
of its dual space and some results on the structure of finitely additive
measures.
Archive classification: math.FA
Mathematics Subject Classification: Primary 28A25, Secondary 46B50
Submitted from: gianluca.cassese at unimib.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.1192
or
http://arXiv.org/abs/1203.1192
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sjoerd Dirksen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:54:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Noncommutative and vector-valued
Boyd interpolation theorems" by Sjoerd Dirksen.
Abstract: We present a new, elementary proof of Boyd's interpolation
theorem. Our approach naturally yields a vector-valued as well as
a noncommutative version of this result and even allows for the
interpolation of certain operators on $l^1$-valued noncommutative
symmetric spaces. By duality we may interpolate several well-known
noncommutative maximal inequalities. In particular we obtain a version of
Doob's maximal inequality and the dual Doob inequality for noncommutative
symmetric spaces. We apply our results to prove the Burkholder-Davis-Gundy
and Burkholder-Rosenthal inequalities for noncommutative martingales in
these spaces.
Archive classification: math.FA math.OA math.PR
Submitted from: sjoerd.dirksen at hcm.uni-bonn.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.1653
or
http://arXiv.org/abs/1203.1653
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Ibort, P. Linares, and J.G. Llavona
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:55:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A representation theorem
for orthogonally additive polynomials in Riesz spaces" by A. Ibort,
P. Linares, and J.G. Llavona.
Abstract: The aim of this article is to prove a representation theorem for
orthogonally additive polynomials in the spirit of the recent theorem on
representation of orthogonally additive polynomials on Banach lattices
but for the setting of Riesz spaces. To this purpose the notion of
$p$--orthosymmetric multilinear form is introduced and it is shown
to be equivalent to the or\-tho\-go\-na\-lly additive property of the
corresponding polynomial. Then the space of positive orthogonally additive
polynomials on an Archimedean Riesz space taking values on an uniformly
complete Archimedean Riesz space is shown to be isomorphic to the space
of positive linear forms on the $n$-power in the sense of Boulabiar and
Buskes of the original Riesz space.
Archive classification: math.FA
Mathematics Subject Classification: 46A40, 46G25, 47B65
Citation: Rev. Mat. Complutense, 25 (1) 21-30 (2012)
Submitted from: albertoi at math.uc3m.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.2379
or
http://arXiv.org/abs/1203.2379
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Ibort, P. Linares, and J.G. Llavona
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:57:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the representation of
orthogonally additive polynomials in $\ell_p$" by A. Ibort, P. Linares,
and J.G. Llavona.
Abstract: We present a new proof of a Sundaresan's result which shows that
the space of orthogonally additive polynomials $\mathcal{P}_o(^k\ell_p)$
is isometrically isomorphic to $\ell_{p/p-k}$ if $k<p<\infty$ and to
$\ell_\infty$ if $1\leq p\leq k$.
Archive classification: math.FA
Mathematics Subject Classification: 46G25, 46B42, 46M05
Citation: Publ. Res. Inst. Math. Sci., 45 (2) 519-24 (2009)
Submitted from: albertoi at math.uc3m.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.2968
or
http://arXiv.org/abs/1203.2968
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yang Cao, Geng Tian, and Bingzhe Hou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:59:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Schauder bases and operator theory"
by Yang Cao, Geng Tian, and Bingzhe Hou.
Abstract: In this paper, we firstly give a matrix approach to the bases
of a separable Hilbert space and then correct a mistake appearing in both
review and the English translation of the Olevskii's paper. After this,
we show that even a diagonal compact operator may map an orthonormal
basis into a conditional basis.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B37, 47B99, Secondary
54H20, 37B99
Remarks: 17 pages
Submitted from: caoyang at jlu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3603
or
http://arXiv.org/abs/1203.3603
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denny H. Leung and Ya-Shu Wang
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:02:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compact and weakly compact
disjointness preserving operators on spaces of differentiable functions"
by Denny H. Leung and Ya-Shu Wang.
Abstract: A pair of functions defined on a set X with values in a
vector space E is said to be disjoint if at least one of the functions
takes the value $0$ at every point in X. An operator acting between
vector-valued function spaces is disjointness preserving if it maps
disjoint functions to disjoint functions. We characterize compact and
weakly compact disjointness preserving operators between spaces of Banach
space-valued differentiable functions.
Archive classification: math.FA
Mathematics Subject Classification: 46E40, 46E50, 47B33, 47B38
Submitted from: matlhh at nus.edu.sg
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3607
or
http://arXiv.org/abs/1203.3607
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stiene Riemer and Carsten Schuett
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:04:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the expectation of the norm
of random matrices with non-identically distributed" by Stiene Riemer
and Carsten Schuett.
Abstract: We give estimates for the expectation of the norm of random
matrices with independent but not necessarily identically distributed
entries.
Archive classification: math.FA
Submitted from: riemer at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3713
or
http://arXiv.org/abs/1203.3713
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno and Stiene Riemer
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:06:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the maximum of random variables
on product spaces" by Joscha Prochno and Stiene Riemer.
Abstract: Let $\xi_i$, $i=1,...,n$, and $\eta_j$,
$j=1,...,m$ be iid p-stable respectively q-stable random
variables, $1<p<q<2$. We prove estimates for $\Ex_{\Omega_1}
\Ex_{\Omega_2}\max_{i,j}\abs{a_{ij}\xi_i(\omega_1)\eta_j(\omega_2)}$ in
terms of the $\ell_p^m(\ell_q^n)$-norm of $(a_{ij})_{i,j}$. Additionally,
for p-stable and standard gaussian random variables we prove estimates
in terms of the $\ell_p^m(\ell_{M_{\xi}}^n)$-norm, $M_{\xi}$ depending
on the Gaussians. Furthermore, we show that a sequence $\xi_i$,
$i=1,\ldots,n$ of iid $\log-\gamma(1,p)$ distributed random variables
($p\geq 2$) generates a truncated $\ell_p$-norm, especially $\Ex
\max_{i}\abs{a_i\xi_i}\sim \norm{(a_i)_i}_2$ for $p=2$. As far as we
know, the generating distribution for $\ell_p$-norms with $p\geq 2$
has not been known up to now.
Archive classification: math.FA math.PR
Remarks: 17 pages
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3788
or
http://arXiv.org/abs/1203.3788
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jeremy Avigad and Jason Rute
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:07:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Oscillation and the mean ergodic
theorem" by Jeremy Avigad and Jason Rute.
Abstract: Let B be a uniformly convex Banach space, let T be a
nonexpansive linear operator, and let A_n x denote the ergodic average
(1/n) sum_{i<n} T^n x. A generalization of the mean ergodic theorem
due to Garrett Birkhoff asserts that the sequence (A_n x) converges,
which is equivalent to saying that for every epsilon > 0, the sequence
has only finitely many fluctuations greater than epsilon. Drawing on
calculations by Kohlenbach and Leustean, we provide a uniform bound
on the number of fluctuations that depends only on rho := || x || /
epsilon and a modulus, eta, of uniform convexity for B. Specifically,
we show that the sequence of averages (A_n x) has O(rho^2 log rho *
eta(1/(8 rho))^{-1})-many epsilon-fluctuations, and if B is a Hilbert
space, the sequence has O(rho^3 log rho)-many epsilon-fluctuations. The
proof is fully explicit, providing a remarkably uniform, quantitative,
and constructive formulation of the mean ergodic theorem.
Archive classification: math.DS math.FA math.LO
Mathematics Subject Classification: 37A30, 03F60
Submitted from: avigad at cmu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.4124
or
http://arXiv.org/abs/1203.4124
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fabio Jose Bertoloto
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:10:26 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Duality of certain Banach spaces
of vector-valued holomorphic functions" by Fabio Jose Bertoloto.
Abstract: In this work we study the vector-valued Hardy spaces H p (D;
F ) (1 ≤ p ≤ ∞) and their relationship with RNP, ARNP and the UMDP
properties. By following the approach of Taylor in the scalar-valued
case, we prove that, when F and F have the ARNP property, then H p (D;
F ) and H q (D; F ) are canonically topologically isomorphic (for p,
q ∈ (1, ∞) conjugate indices) if and only if F has the UMDP.
Archive classification: math.FA
Mathematics Subject Classification: 46G20, 46G10, 30H10
Submitted from: bertoloto at famat.ufu.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.5322
or
http://arXiv.org/abs/1203.5322
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Casey Kelleher, Daniel Miller, Trenton
Osborn and Anthony Weston
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 15:56:02 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Polygonal equalities and virtual
degeneracy in $L$-spaces" by Casey Kelleher, Daniel Miller, Trenton
Osborn and Anthony Weston.
Abstract: Cases of equality in the classical $p$-negative type
inequalities for $L_{p}(\mu)$-spaces are characterized for each $p \in
(0,2)$ according to a new property called virtual degeneracy. For each
$p \in (0,2)$, this leads to a complete classification of the subsets of
$L_{p}$-spaces that have strict $p$-negative type. It follows that if $0 <
p < q \leq 2$ and if $(\Omega_{1}, \mu_{1})$ and $(\Omega_{2}, \mu_{2})$
are measure spaces, then no subset of $L_{q}(\Omega_{2}, \mu_{2})$ is
isometric to any linear subspace $W$ of $L_{p}(\Omega_{1}, \mu_{1})$
that contains a pair of disjointly supported unit vectors. Under these
circumstances it is also the case that no subset of $L_{q}(\Omega_{2},
\mu_{2})$ is isometric to any subset of $L_{p}(\Omega_{1}, \mu_{1})$
that has non-empty interior. We conclude the paper by examining virtually
degenerate subspaces of $L_{p}(\mu)$-spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Remarks: 9 pages
Submitted from: westona at canisius.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.5837
or
http://arXiv.org/abs/1203.5837
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 15:57:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Global and local boundedness of
Polish groups" by Christian Rosendal.
Abstract: We present a comprehensive theory of boundedness properties
for Polish groups developed with a main focus on Roelcke precompactness
(precompactness of the lower uniformity) and Property (OB) (boundedness of
all isometric actions on separable metric spaces). In particular, these
properties are characterised by the orbit structure of isometric actions
on metric spaces and isometric or continuous affine representations on
separable Banach spaces.
Archive classification: math.FA math.GR
Mathematics Subject Classification: Primary: 22A25, Secondary: 03E15,
46B04
Submitted from: rosendal at math.uic.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.6047
or
http://arXiv.org/abs/1203.6047
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mohammad Sadegh Asgari
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:03:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New characterizations of fusion
bases and Riesz fusion bases in hilbert spaces" by Mohammad Sadegh Asgari.
Abstract: In this paper we investigate a new notion of bases in Hilbert
spaces and similar to fusion frame theory we introduce fusion bases
theory in Hilbert spaces. We also introduce a new definition of fusion
dual sequence associated with a fusion basis and show that the operators
of a fusion dual sequence are continuous projections. Next we define
the fusion biorthogonal sequence, Bessel fusion basis, Hilbert fusion
basis and obtain some characterizations of them. we study orthonormal
fusion systems and Riesz fusion bases for Hilbert spaces. we consider the
stability of fusion bases under small perturbations. We also generalized
a result of Paley-Wiener [13] to the situation of fusion basis.
Archive classification: math.FA
Mathematics Subject Classification: Primary 42C15, Secondary 46C99
Remarks: 14 pages
Submitted from: moh.asgari at iauctb.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.6279
or
http://arXiv.org/abs/1203.6279
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eli Glasner and Michael Megrelishvili
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:05:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Banach representations and affine
compactifications of dynamical systems" by Eli Glasner and Michael
Megrelishvili.
Abstract: To every Banach space V we associate a compact right
topological affine semigroup E(V). We show that a separable Banach space
V is Asplund if and only if E(V) is metrizable, and it is Rosenthal
(i.e. it does not contain an isomorphic copy of $l_1$) if and only if
E(V) is a Rosenthal compactum. We study representations of compact right
topological semigroups in E(V). In particular, representations of tame
and HNS-semigroups arise naturally as enveloping semigroups of tame and
HNS (hereditarily non-sensitive) dynamical systems, respectively. As an
application we obtain a generalization of a theorem of R. Ellis. A main
theme of our investigation is the relationship between the enveloping
semigroup of a dynamical system X and the enveloping semigroup of its
various affine compactifications Q(X). When the two coincide we say that
the affine compactification Q(X) is E-compatible. This is a refinement of
the notion of injectivity. We show that distal non-equicontinuous systems
do not admit any E-compatible compactification. We present several new
examples of non-injective dynamical systems and examine the relationship
between injectivity and E-compatibility.
Archive classification: math.DS math.FA math.GN
Remarks: 43 pages
Submitted from: megereli at math.biu.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.0432
or
http://arXiv.org/abs/1204.0432
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Barvinok
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:07:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximations of convex bodies
by polytopes and by projections of spectrahedra" by Alexander Barvinok.
Abstract: We prove that for any compact set B in R^d and for any epsilon
>0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points
such that the maximum absolute value of any linear function ell: R^d
--> R on X approximates the maximum absolute value of ell on B within
a factor of epsilon sqrt{d}. We also prove that for any finite set B
in Z^d and for any positive integer k there is a convex set C in R^d
containing B such that C is an affine image of a section of the cone of
rxr positive semidefinite matrices for r=d^{O(k)} and such that for any
linear function ell: R^d --> R with integer coefficients the maximum
absolute value of ell on B and the maximum absolute value of ell on C
coincide provided the former does not exceed k.
Archive classification: math.MG math.FA math.OC
Mathematics Subject Classification: 52A20, 52A27, 52A21, 52B55, 90C22
Remarks: 11 pages
Submitted from: barvinok at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.0471
or
http://arXiv.org/abs/1204.0471
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rogerio Fajardo, Pedro Kaufmann and
Leonardo Pellegrini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:09:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spaceability in sets of operators
on $C(K)$" by Rogerio Fajardo, Pedro Kaufmann and Leonardo Pellegrini.
Abstract: We prove that if $K$ is a compact Hausdorff space satisfying
either condition \item $K$ contains a nontrivial convergent sequence,
or \item $C(K)$ is isomorphic to its square, then there exists an
infinite-dimensional closed subspace of the space of operators on $C(K)$,
each nonzero element of which does \emph{not} have the form $gI+S$,
where $g\in C(K)$, $S$ is weakly compact and $I$ is the identity
operator. This comes in contrast with what happens in $C(K)$ spaces
with \emph{few operators} in the sense of Koszmider [P. Koszmider,
P., Banach spaces of continuous functions with few operators. Math.
Ann. 300 (2004), no. 1, 151 - 183.], which are precisely $C(K)$ spaces
where \emph{every} operator is of the form $gI+S$.
In addition we show that, in case $C(K)$ has few operators, there is an
opertator $J$ on $C(K\times\{0,1\})=C(K)^2$ such that each operator
on $C(K\times\{0,1\})$ is of the form $gI+hJ+S$, where $g,h\in
C(K\times\{0,1\})$ and $S$ is strictly singular, in connection to a
result by Ferenczi [V. Ferenczi,Uniqueness of complex structure and
real hereditarily indecomposable Banach spaces. Adv. Math. 213 (2007),
no. 1, 462 - 488.].
Archive classification: math.FA
Submitted from: leoime at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.6855
or
http://arXiv.org/abs/1203.6855
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Soeren Christensen, Joscha Prochno, and
Stiene Riemer
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:13:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An inversion formula for Orlicz
norms and sequences of random variables" by Soeren Christensen, Joscha
Prochno, and Stiene Riemer.
Abstract: Given an Orlicz function $M$, we show which random variables
$\xi_i$, $i=1,...,n$ generate the associated Orlicz norm, i.e., which
random variables yield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_i\xi_i|
\sim \norm{(x_i)_{i=1}^n}_M$. As a corollary we obtain a representation
for the distribution function in terms of $M$ and $M'$ which can be
easily applied to many examples of interest.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 46B09, 60E15
Remarks: 11 pages
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.1242
or
http://arXiv.org/abs/1204.1242
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Afonso S. Bandeira, Edgar Dobriban, Dustin
G. Mixon, and William F. Sawin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:15:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Certifying the restricted isometry
property is hard" by Afonso S. Bandeira, Edgar Dobriban, Dustin G. Mixon,
and William F. Sawin.
Abstract: This paper is concerned with an important matrix condition in
compressed sensing known as the restricted isometry property (RIP). We
demonstrate that testing whether a matrix satisfies RIP is hard for
NP under randomized polynomial-time reductions. Our reduction is from
the NP-complete clique decision problem, and it uses ideas from matroid
theory. As a consequence of our result, it is impossible to efficiently
test for RIP provided NP \not\subseteq BPP, an assumption which is
slightly stronger than P \neq NP.
Archive classification: math.FA cs.IT math.IT
Remarks: 7 pages
Submitted from: dmixon at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.1580
or
http://arXiv.org/abs/1204.1580
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Geng Tian, Youqing Ji, and Yang Cao
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:17:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Schauder bases and operator theory
II: (SI) Schauder operators" by Geng Tian, Youqing Ji, and Yang Cao.
Abstract: In this paper, we will show that for an operator $T$ which is
injective and has dense range, there exists an invertible operator $X$
(in fact we can find $U+K$, where $U$ is an unitary operator and $K$
is a compact operator with norm less than a given positive real number)
such that $XT$ is strongly irreducible. As its application, strongly
irreducible operators always exist in the orbit of Schauder matrices.
Archive classification: math.FA
Mathematics Subject Classification: 47A55, 47A53, 47A16, Secondary 54H20
Remarks: It is the 3rd version of our paper
Submitted from: caoyang at jlu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.1587
or
http://arXiv.org/abs/1204.1587
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Joram lindenstrauss
From: Dale Alspach <alspach at math.okstate.edu>
Date: Sun, 29 Apr 2012 14:43:24 -0500
To: banach at math.okstate.edu
Joram Lindenstrauss died today after a long illness.
His influence on Banach space theory has been enormous.
Personally, I benefited from his visits to Ohio State while I was a
graduate student and early on learned much from his books written with Lior
Tzafriri.
Dale Alspach
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean-Matthieu Auge
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:36:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Linear operators with wild
dynamics" by Jean-Matthieu Auge.
Abstract: If $X$ is a separable infinite dimensional Banach space, we
construct a bounded and linear operator $R$ on $X$ such that $$ A_R=\{x
\in X, \|R^tx\| \rightarrow \infty\} $$ is not dense and has non empty
interior with the additional property that $R$ can be written $I+K$,
where $I$ is the identity and $K$ is a compact operator. This answers
two recent questions of H\'ajek and Smith.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47A05, Secondary 47A15, 47A16
Remarks: 14 pages
Submitted from: jean-matthieu.auge at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2044
or
http://arXiv.org/abs/1204.2044
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean-Matthieu Auge
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:38:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Orbits of linear operators and
Banach space geometry" by Jean-Matthieu Auge.
Abstract: Let $T$ be a bounded linear operator on a (real or complex)
Banach space $X$. If $(a_n)$ is a sequence of non-negative numbers
tending to 0. Then, the set of $x \in X$ such that $\|T^nx\| \geqslant
a_n \|T^n\|$ for infinitely many $n$'s has a complement which is both
$\sigma$-porous and Haar-null. We also compute (for some classical
Banach space) optimal exponents $q>0$, such that for every non nilpotent
operator $T$, there exists $x \in X$ such that $(\|T^nx\|/\|T^n\|)
\notin \ell^{q}(\mathbb{N})$, using techniques which involve the modulus
of asymptotic uniform smoothness of $X$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47A05, 47A16, Secondary 28A05
Remarks: 16 pages
Submitted from: jean-matthieu.auge at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2046
or
http://arXiv.org/abs/1204.2046
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean-Matthieu Auge
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:39:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Perturbation of farthest points
in weakly compact sets" by Jean-Matthieu Auge.
Abstract: If $f$ is a real valued weakly lower semi-continous function
on a Banach space $X$ and $C$ a weakly compact subset of $X$, we show
that the set of $x \in X$ such that $z \mapsto \|x-z\|-f(z)$ attains its
supremum on $C$ is dense in $X$. We also construct a counter example
showing that the set of $x \in X$ such that $z \mapsto \|x-z\|+\|z\|$
attains its supremum on $C$ is not always dense in $X$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 41A65
Remarks: 5 pages
Submitted from: jean-matthieu.auge at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2047
or
http://arXiv.org/abs/1204.2047
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:41:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A remark on condensation of
singularities" by Jan-David Hardtke.
Abstract: Recently Alan D. Sokal gave a very short and completely
elementary proof of the uniform boundedness principle. The aim of this
note is to point out that by using a similiar technique one can give a
considerably short and simple proof of a stronger statement, namely a
principle of condensation of singularities for certain double-sequences
of non-linear operators on quasi-Banach spaces, which is a bit more
general than a result of I.\,S. G\'al.
Archive classification: math.FA
Mathematics Subject Classification: 46A16, 47H99
Remarks: 7 pages
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2106
or
http://arXiv.org/abs/1204.2106
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. Botelho, D. Cariello, V.V. Favaro, D.
Pellegrino and J.B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:43:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Subspaces
of maximal dimension contained in $L_{p}(\Omega)
- \textstyle\bigcup\limits_{q<p}L_{q}(\Omega)$}" by G. Botelho,
D. Cariello, V.V. Favaro, D. Pellegrino and J.B. Seoane-Sepulveda.
Abstract: Let $(\Omega,\Sigma,\mu)$ be a measure space and $1< p <
+\infty$. In this paper we determine when the set $L_{p}(\Omega) -
\bigcup\limits_{1 \leq q < p}L_{q}(\Omega)$ is maximal spaceable, that is,
when it contains (except for the null vector) a closed subspace $F$ of
$L_{p}(\Omega)$ such that $\dim(F) = \dim\left(L_{p}(\Omega)\right)$. The
aim of the results presented here is, among others, to generalize all the
previous work (since the 1960's) related to the linear structure of the
sets $L_{p}(\Omega) - L_{q}(\Omega)$ with $q < p$ and $L_{p}(\Omega) -
\bigcup\limits_{1 \leq q < p}L_{q}(\Omega)$. We shall also give examples,
propose open questions and provide new directions in the study of maximal
subspaces of classical measure spaces.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2170
or
http://arXiv.org/abs/1204.2170
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ronald DeVore, Guergana Petrova, and
Przemyslaw Wojtaszczyk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:44:34 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Greedy algorithms for reduced
bases in Banach spaces" by Ronald DeVore, Guergana Petrova, and Przemyslaw
Wojtaszczyk.
Abstract: Given a Banach space X and one of its compact sets F,
we consider the problem of finding a good n dimensional space X_n
⊂ X which can be used to approximate the elements of F. The best
possible error we can achieve for such an approximation is given by
the Kolmogorov width d_n(F)_X. However, finding the space which gives
this performance is typically numerically intractable. Recently, a
new greedy strategy for obtaining good spaces was given in the context
of the reduced basis method for solving a parametric family of PDEs.
The performance of this greedy algorithm was initially analyzed in
A. Buffa, Y. Maday, A.T. Patera, C. Prud’homme, and G. Turinici,
''A Priori convergence of the greedy algorithm for the parameterized
reduced basis'', M2AN Math. Model. Numer. Anal., 46(2012), 595–603 in
the case X = H is a Hilbert space. The results there were significantly
improved on in P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova,
and P. Wojtaszczyk, ''Convergence rates for greedy algorithms in reduced
bases Methods'', SIAM J. Math. Anal., 43 (2011), 1457–1472. The purpose
of the present paper is to give a new analysis of the performance of
such greedy algorithms. Our analysis not only gives improved results
for the Hilbert space case but can also be applied to the same greedy
procedure in general Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 41A46, 41A25, 46B20, 15A15
Submitted from: gpetrova at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2290
or
http://arXiv.org/abs/1204.2290
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S Dutta and A B Abubaker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:45:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Generalized 3-circular projections
in some Banach spaces" by S Dutta and A B Abubaker.
Abstract: Recently in a series of papers it is observed that in
many Banach spaces, which include classical spaces $C(\Omega)$
and $L_p$-spaces, $1 \leq p < \infty, p \neq 2$, any generalized
bi-circular projection $P$ is given by $P = \frac{I+T}{2}$, where
$I$ is the identity operator of the space and $T$ is a reflection,
that is, $T$ is a surjective isometry with $T^2 = I$. For surjective
isometries of order $n \geq 3$, the corresponding notion of projection
is generalized $n$-circular projection as defined in \cite{AD}. In this
paper we show that in a Banach space $X$, if generalized bi-circular
projections are given by $\frac{I+T}{2}$ where $T$ is a reflection,
then any generalized $n$-circular projection $P$, $n \geq 3$, is given
by $P = \frac{I+T+T^2+\cdots+T^{n-1}}{n}$ where $T$ is a surjective
isometry and $T^n = I$. We prove our results for $n=3$ and for $n > 3$,
the proof remains same except for routine modifications.
Archive classification: math.FA
Mathematics Subject Classification: 47L05, 46B20
Remarks: 8 pages
Submitted from: sudipta at iitk.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2360
or
http://arXiv.org/abs/1204.2360
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Taras Banakh, Bogdan Bokalo, and Nadiya
Kolos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:47:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On \sigma-convex subsets in spaces
of scatteredly continuous functions" by Taras Banakh, Bogdan Bokalo,
and Nadiya Kolos.
Abstract: We prove that for any topological space $X$ of countable
tightness, each \sigma-convex subspace $\F$ of the space $SC_p(X)$
of scatteredly continuous real-valued functions on $X$ has network
weight $nw(\F)\le nw(X)$. This implies that for a metrizable separable
space $X$, each compact convex subset in the function space $SC_p(X)$ is
metrizable. Another corollary says that two Tychonoff spaces $X,Y$ with
countable tightness and topologically isomorphic linear topological spaces
$SC_p(X)$ and $SC_p(Y)$ have the same network weight $nw(X)=nw(Y)$. Also
we prove that each zero-dimensional separable Rosenthal compact
space is homeomorphic to a compact subset of the function space
$SC_p(\omega^\omega)$ over the space $\omega^\omega$ of irrationals.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 46A55, 46E99, 54C35
Remarks: 6 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2438
or
http://arXiv.org/abs/1204.2438
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fedor Sukochev and Anna Tomskova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:48:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "(E,F)-multipliers and applications"
by Fedor Sukochev and Anna Tomskova.
Abstract: For two given symmetric sequence spaces $E$ and $F$ we study
the $(E,F)$-multiplier space, that is the space all of matrices $M$ for
which the Schur product $M\ast A$ maps $E$ into $F$ boundedly whenever
$A$ does. We obtain several results asserting continuous embedding of
$(E,F)$-multiplier space into the classical $(p,q)$-multiplier space
(that is when $E=l_p$, $F=l_q$). Furthermore, we present many examples
of symmetric sequence spaces $E$ and $F$ whose projective and injective
tensor products are not isomorphic to any subspace of a Banach space with
an unconditional basis, extending classical results of S. Kwapie\'{n} and
A. Pe{\l}czy\'{n}ski and of G. Bennett for the case when $E=l_p$, $F=l_q$.
Archive classification: math.FA
Remarks: 16 pages
Submitted from: tomskovaanna at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2623
or
http://arXiv.org/abs/1204.2623
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by B. de Pagter and A.W. Wickstead
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:49:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Free and projective Banach
lattices" by B. de Pagter and A.W. Wickstead.
Abstract: We define and prove the existence of free Banach lattices in
the category of Banach lattices and contractive lattice homomorphisms and
establish some of their fundamental properties. We give much more detailed
results about their structure in the case that there are only a finite
number of generators and give several Banach lattice characterizations of
the number of generators being, respectively, one, finite or countable. We
define a Banach lattice $P$ to be projective if whenever $X$ is a Banach
lattice, $J$ a closed ideal in $X$, $Q:X\to X/J$ the quotient map,
$T:P\to X/J$ a linear lattice homomorphism and $\epsilon>0$ there is
a linear lattice homomorphism $\hat{T}:P\to X$ such that (i) $T=Q\circ
\hat{T}$ and (ii) $\|\hat{T}\|\le (1+\epsilon)\|T\|$. We establish the
connection between projective Banach lattices and free Banach lattices
and describe several families of Banach lattices that are projective as
well as proving that some are not.
Archive classification: math.FA
Submitted from: A.Wickstead at qub.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4282
or
http://arXiv.org/abs/1204.4282
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:51:26 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantification of the reciprocal
Dunford-Pettis property" by Ondrej F.K. Kalenda and Jiri Spurny.
Abstract: We prove in particular that Banach spaces of the form
$C_0(\Omega)$, where $\Omega$ is a locally compact space, enjoy a
quantitative version of the reciprocal Dunford-Pettis property.
Archive classification: math.FA
Remarks: 16 pages
Submitted from: kalenda at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4308
or
http://arXiv.org/abs/1204.4308
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Laurent W. Marcoux, Alexey I. Popov, and
Heydar Radjavi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:53:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On almost-invariant subspaces
and approximate commutation" by Laurent W. Marcoux, Alexey I. Popov,
and Heydar Radjavi.
Abstract: A closed subspace of a Banach space $\cX$ is almost-invariant
for a collection $\cS$ of bounded linear operators on $\cX$ if for each $T
\in \cS$ there exists a finite-dimensional subspace $\cF_T$ of $\cX$ such
that $T \cY \subseteq \cY + \cF_T$. In this paper, we study the existence
of almost-invariant subspaces of infinite dimension and codimension for
various classes of Banach and Hilbert space operators. We also examine
the structure of operators which admit a maximal commuting family of
almost-invariant subspaces. In particular, we prove that if $T$ is an
operator on a separable Hilbert space and if $TP-PT$ has finite rank for
all projections $P$ in a given maximal abelian self-adjoint algebra $\fM$
then $T=M+F$ where $M\in\fM$ and $F$ is of finite rank.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47A15, 47A46, 47B07, 47L10
Submitted from: a4popov at uwaterloo.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4621
or
http://arXiv.org/abs/1204.4621
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Wayne Lawton
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:55:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spectral envelopes - A preliminary
report" by Wayne Lawton.
Abstract: The spectral envelope S(F) of a subset of integers is the set
of probability measures on the circle group that are weak star limits of
squared moduli of trigonometric polynomials with frequencies in F. Fourier
transforms of these measures are positive and supported in F - F but the
converse generally fails. The characteristic function chiF of F is a
binary sequence whose orbit closure gives a symbolic dynamical system
O(F). Analytic properties of S(F) are related to dynamical properties
of chiF. The Riemann-Lebesque lemma implies that if chiF is minimal,
then S(F) is convex and hence S(F) is the closure of the convex hull of
its extreme points Se(F). In this paper we (i) review the relationship
between these concepts and the special case of the still open 1959
Kadison-Singer problem called Feichtinger's conjecture for exponential
functions, (ii) partially characterize of elements in Se(F), for minimal
chiF, in terms of ergodic properties of (O(F),lambda) where lambda is a
shift invariant probability measure whose existence in ensured by the 1937
Krylov-Bogoyubov theorem, (iii) refine previous numerical studies of the
Morse-Thue minimal binary sequence by exploiting a new MATLAB algorithm
for computing smallest eigenvalues of 4,000,000 x 4,000,000 matrices,
(iv) describe recent results characterizing S(F) for certain Bohr sets F
related to quasicrystals, (v) extend these concepts to general discrete
groups including those with Kazhdan's T-property, such as SL(n,Z), n >
2, which can be characterized by several equivalent properties such as:
any sequence of positive definite functions converging to 1 uniformly on
compact subsets converges uniformly. This exotic property may be useful
to construct a counterexample to the generalization of Feichtinger's
conjecture and hence to provide a no answer to the question of Kadison
and Singer whcih they themselves tended to suspect.
Archive classification: math.FA
Mathematics Subject Classification: 37B10, 42A55, 43A35
Remarks: To appear in Proceedings the Annual Meeting in Mathematics,
Bangkok,
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4904
or
http://arXiv.org/abs/1204.4904
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:56:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sharp coincidences for absolutely
summing multilinear operators" by Daniel Pellegrino.
Abstract: In this note we prove the optimality of a family of known
coincidence theorems for absolutely summing multilinear operators. We
connect our results with the theory of multiple summing multilinear
operators and prove the sharpness of similar results obtained via the
complex interpolation method.
Archive classification: math.FA
Remarks: This note is part of the author's thesis which is being
written for
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.5411
or
http://arXiv.org/abs/1204.5411
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tao Mei
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:59:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A universal $H_1$-BMO duality
theory for semigroups of operators" by Tao Mei.
Abstract: Let (M,\mu) be a sigma-finite measure space. Let (T_t)
be a semigroup of positive preserving maps on (M,\mu) with standard
assumptions. We prove a $H_1$-BMO duality theory with assumptions only
on the semigroup of operators. The H1's are defined by square functions
of P. A. Meyer's gradient form. The formulation of the assumptions does
not rely on any geometric/metric property of M nor on the kernel of the
semigroups of operators. Our main results extend to the noncommutative
setting as well, e.g. the case where $L_\infty(M,\mu)$ is replaced by
von Neuman algebras with a semifinite trace. We also prove a Carlson
embedding theorem for semigroups of operators.
Archive classification: math.CA math.FA math.OA
Mathematics Subject Classification: 46L51 42B25 46L10 47D06
Remarks: 22 pages
Submitted from: mei at wayne.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.4424
or
http://arXiv.org/abs/1005.4424
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. Botelho, D. Pellegrino, P. Rueda, J.
Santos and J.B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 15:56:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "When is the Haar measure a Pietsch
measure for nonlinear mappings?" by G. Botelho, D. Pellegrino, P. Rueda,
J. Santos and J.B. Seoane-Sepulveda.
Abstract: We show that, as in the linear case, the normalized Haar measure
on a compact topological group $G$ is a Pietsch measure for nonlinear
summing mappings on closed translation invariant subspaces of $C(G)$. This
answers a question posed to the authors by J. Diestel. We also show that
our result applies to several well-studied classes of nonlinear summing
mappings. In the final section some problems are proposed.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.5621
or
http://arXiv.org/abs/1204.5621
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno and Carsten Schuett
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 15:58:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Combinatorial inequalities and
subspaces of L1" by Joscha Prochno and Carsten Schuett.
Abstract: Let M and N be Orlicz functions. We establish some combinatorial
inequalities and show that the product spaces l^n_M(l^n_N) are uniformly
isomorphic to subspaces of L_1 if M and N are "separated" by a function
t^r, 1<r<2.
Archive classification: math.FA math.CO
Mathematics Subject Classification: 46B03, 05A20, 46B45, 46B09
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.6025
or
http://arXiv.org/abs/1204.6025
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 15:59:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The embedding of 2-concave
Musielak-Orlicz spaces into L_1 via l_2-matrix-averages" by Joscha
Prochno.
Abstract: In this note we prove that $\frac{1}{n!} \sum_{\pi} (
\sum_{i=1}^n |x_i a_{i,\pi(i)} |^2)^{\frac{1}{2}}$ is equivalent to a
Musielak-Orlicz norm $\norm{x}_{\sum M_i}$. We also obtain the inverse
result, i.e., given the Orlicz functions, we provide a formula for the
choice of the matrix that generates the corresponding Musielak-Orlicz
norm. As a consequence, we obtain the embedding of strictly 2-concave
Musielak-Orlicz spaces into L_1.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 05A20, 46B45
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.6030
or
http://arXiv.org/abs/1204.6030
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Szymon Glab, Pedro L. Kaufmann and Leonardo
Pellegrini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:00:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spaceability and algebrability of
sets of nowhere integrable functions" by Szymon Glab, Pedro L. Kaufmann
and Leonardo Pellegrini.
Abstract: We show that the set of Lebesgue integrable functions
in $[0,1]$ which are nowhere essentially bounded is spaceable,
improving a result from [F. J. Garc\'{i}a-Pacheco, M. Mart\'{i}n,
and J. B. Seoane-Sep\'ulveda. \textit{Lineability, spaceability,
and algebrability of certain subsets of function spaces,} Taiwanese
J. Math., \textbf{13} (2009), no. 4, 1257--1269], and that it is strongly
$\mathfrak{c}$-algebrable. We prove strong $\mathfrak{c}$-algebrability
and non-separable spaceability of the set of functions of bounded
variation which have a dense set of jump discontinuities. Applications to
sets of Lebesgue-nowhere-Riemann integrable and Riemann-nowhere-Newton
integrable functions are presented as corollaries. In addition
we prove that the set of Kurzweil integrable functions which are
not Lebesgue integrable is spaceable (in the Alexievicz norm)
but not $1$-algebrable. We also show that there exists an infinite
dimensional vector space $S$ of differentiable functions such that
each element of the $C([0,1])$-closure of $S$ is a primitive to a
Kurzweil integrable function, in connection to a classic spaceability
result from [V. I. Gurariy, \textit{Subspaces and bases in spaces of
continuous functions (Russian),} Dokl. Akad. Nauk SSSR, \textbf{167}
(1966), 971--973].
Archive classification: math.FA
Remarks: accepted on 2011
Submitted from: leoime at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.6404
or
http://arXiv.org/abs/1204.6404
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas P. Hytonen and Michael T. Lacey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:02:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Pointwise convergence of
vector-valued Fourier series" by Tuomas P. Hytonen and Michael T. Lacey.
Abstract: We prove a vector-valued version of Carleson's theorem:
Let Y=[X,H]_t be a complex interpolation space between a UMD space
X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the
partial sums of the Fourier series of f converge to f pointwise almost
everywhere. Apparently, all known examples of UMD spaces are of this
intermediate form Y=[X,H]_t. In particular, we answer affirmatively a
question of Rubio de Francia on the pointwise convergence of Fourier
series of Schatten class valued functions.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 42B20, 42B25
Remarks: 26 pages
Submitted from: tuomas.hytonen at helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.0261
or
http://arXiv.org/abs/1205.0261
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
Title: Estimating support functions of random polytopes via Orlicz norms
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:09:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Estimating support functions of
random polytopes via Orlicz norms" by David Alonso-Gutierrez and Joscha
Prochno.
Abstract: We study the expected value of support functions of random
polytopes in a certain direction, where the random polytope is given
by independent random vectors uniformly distributed in an isotropic
convex body. All results are obtained by an utterly novel approach,
using probabilistic estimates in connection with Orlicz norms that were
not used in this connection before.
Archive classification: math.FA
Mathematics Subject Classification: Primary 52A22, Secondary 52A23,
05D40, 46B09
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.2023
or
http://arXiv.org/abs/1205.2023
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ioannis Gasparis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:14:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A new isomorphic \ell_1 predual
not isomorphic to a complemented subspace of a C(K) space" by Ioannis
Gasparis.
Abstract: An isomorphic \(\ell_1\)-predual space \(X\) is constructed
such that neither \(X\) is isomorphic to a subspace of \(c_0\), nor
\(C(\omega^\omega)\) is isomorphic to a subspace of \(X\). It follows that
\(X\) is not isomorphic to a complemented subspace of a \(C(K)\) space.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Remarks: 12 pages
Submitted from: ioagaspa at math.auth.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/mod/1205.4317
or
http://arXiv.org/abs/mod/1205.4317
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:16:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An introduction to the Ribe
program" by Assaf Naor.
Abstract: This article accompanies the 10th Takagi Lectures, delivered
by the author at RIMS, Kyoto, on May 26 2012. It contains an exposition
of results, applications, and challenges of the Ribe program.
Archive classification: math.FA math.MG
Remarks: To appear in Japanese Journal of Mathematics
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.5993
or
http://arXiv.org/abs/1205.5993
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:17:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Gaussian behavior
of marginals and the mean width of random polytopes" by David
Alonso-Gutierrez and Joscha Prochno.
Abstract: We show that the expected value of the mean width of a random
polytope generated by $N$ random vectors ($n\leq N\leq e^{\sqrt n}$)
uniformly distributed in an isotropic convex body in $\R^n$ is of
the order $\sqrt{\log N} L_K$. This completes a result of Dafnis,
Giannopoulos and Tsolomitis. We also prove some results in connection
with the 1-dimensional marginals of the uniform probability measure on
an isotropic convex body, extending the interval in which the average
of the distribution functions of those marginals behaves in a sub-
or supergaussian way.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 52A22, 52A23, 05D40, 46B09
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.6174
or
http://arXiv.org/abs/1205.6174
Return-path: <banach-bounces at math.okstate.edu>
Subject: [Banach] SUMIRFAS announcement
From: Bill Johnson <johnson at math.tamu.edu>
Date: Thu, 21 Jun 2012 16:57:58 -0500 (CDT)
To: banach at math.okstate.edu
1st ANNOUNCEMENT OF SUMIRFAS 2012
The Informal Regional Functional Analysis Seminar
August 3-5
Texas A&M University, College Station
Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis
and Probability page, whose NEW URL is
http://www.math.tamu.edu/~kerr/workshop/
The first talk will be in the early afternoon on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 169. The
Blocker Building is on Ireland St. just south of University Dr. on the
Texas A&M campus:
http://www.math.tamu.edu/contact/blocker.html.
Coffee and refreshments will be available in Blocker 148.
Speakers at SUMIRFAS 2012 include
Pete Casazza
Ed Effros
Su Gao
Ali Kavruk
Masoud Khalkhali
Izabella Laba
Michael Lacey
Paul Mueller
Darrin Speegle
Russ Thompson
July 16 - 19 there will be a Concentration Week on "Frame Theory and Maps
Between Operator Algebras",
organized by Chris Heil, Emily J. King (chair), Keri Kornelson, and Darrin
Speegle. A researcher working in frame theory will naturally be led to
consider matrices (the Gram matrix, the analysis operator and the
synthesis operator), and many problems in frame theory have a re-casting
in operator theory. The most celebrated example of this is the
Kadison-Singer problem. By now, there are many mathematicians familiar
with the basics of the two areas, and there is a fruitful collaboration.
Less obvious is the relationship between frame theory and maps between
operator algebras. Very recent work in this area by Han, Larson, Lu, and
Lu indicate that this may be a relationship that is ripe for exploiting.
The goal of this concentration week is to bring together researchers in
these two fields so that they may learn from one another and build
networks of potential collaborators. There will be introductory series of
talks on "Frame theory" by Ole Christensen, on "Maps on Operator Algebras"
by Vern Paulsen, and on "Bridging the Gap Between Frame Theory and Maps on
Operator Algebras" by Deguang Han. This concentration week will also lead
into a separate conference on the following weekend celebrating the 70th
birthday of David Larson. The home page for this Workshop is at
http://page.math.tu-berlin.de/~king/cw.html
August 6-10 there will be a Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory",
organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and
Alexei Poltoratski. This CW is designed to bring together two groups of
experts: those specializing in complex and harmonic analysis and those
working in spectral theory of differential operators and mathematical
physics. The main goals of the CW are to study new relationships and to
widen further participation in this area in the United States.
Introductory series of lectures by Stephen Gustafson, Svetlana
Jitomirskaya, Helge Krueger, and Brett Wick are planned
to acquaint non-experts with these topics with the reasonable expectation
that some the participants in the larger Workshop will will be attracted
to this program and inject new ideas into the area.
The home page for this Workshop is at
http://www.math.tamu.edu/~comech/events/hast-2012/
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Frame Theory and Maps
Between Operator Algebras" contact Emily King <eking at math.umd.edu>
For information about the Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory" contact
Constanze Liaw <conni at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Franck Barthe, Karoly J. Boroczky, and
Matthieu Fradelizi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:12:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stability of the functional forms
of the Blaschke-Santalo inequality" by Franck Barthe, Karoly J. Boroczky,
and Matthieu Fradelizi.
Abstract: Stability versions of the functional forms of the
Blaschke-Santalo inequality due to Ball, Artstein-Klartag-Milman,
Fradelizi-Meyer and Lehec are proved.
Archive classification: math.MG math.FA
Submitted from: carlos at renyi.hu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.0369
or
http://arXiv.org/abs/1206.0369
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros, Antonis Manoussakis, and
Anna Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:13:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A type (4) space in
(FR)-classification" by Spiros A. Argyros, Antonis Manoussakis, and
Anna Pelczar-Barwacz.
Abstract: We present a reflexive Banach space with an unconditional
basis which is quasi-minimal and tight by range, i.e. of type (4) in
Ferenczi-Rosendal list within the framework of Gowers' classification
program of Banach spaces. The space is an unconditional variant of the
Gowers Hereditarily Indecomposable space with asymptotically unconditional
basis.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Remarks: 14 pages
Submitted from: anna.pelczar at im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.0651
or
http://arXiv.org/abs/1206.0651
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pierre Youssef
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:15:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Restricted Invertibility and the
Banach-Mazur distance to the cube" by Pierre Youssef.
Abstract: We prove a normalized version of the restricted invertibility
principle obtained by Spielman-Srivastava. Applying this result, we
get a new proof of the proportional Dvoretzky-Rogers factorization
theorem recovering the best current estimate. As a consequence, we
also recover the best known estimate for the Banach-Mazur distance
to the cube: the distance of every n-dimensional normed space from
\ell_{\infty }^n is at most (2n)^(5/6). Finally, using tools from the
work of Batson-Spielman-Srivastava, we give a new proof for a theorem
of Kashin-Tzafriri on the norm of restricted matrices.
Archive classification: math.FA
Submitted from: pierre.youssef at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.0654
or
http://arXiv.org/abs/1206.0654
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergey V. Astashkin, Lech Maligranda and
Konstantin E. Tikhomirov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:16:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New examples of K-monotone weighted
Banach couples" by Sergey V. Astashkin, Lech Maligranda and Konstantin
E. Tikhomirov.
Abstract: Some new examples of K-monotone couples of the type (X,
X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0,
1], are presented. Based on the property of the w-decomposability of a
symmetric space we show that, if a weight w changes sufficiently fast,
all symmetric spaces X with non-trivial Boyd indices such that the Banach
couple (X, X(w)) is K-monotone belong to the class of ultrasymmetric
Orlicz spaces. If, in addition, the fundamental function of X is t^{1/p}
for some p \in [1, \infty], then X = L_p. At the same time a Banach
couple (X, X(w)) may be K-monotone for some non-trivial w in the case
when X is not ultrasymmetric. In each of the cases where X is a Lorentz,
Marcinkiewicz or Orlicz space we have found conditions which guarantee
that (X, X(w)) is K-monotone.
Archive classification: math.FA
Mathematics Subject Classification: Functional Analysis (math.FA)
Remarks: 31 pages
Submitted from: lech.maligranda at ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1244
or
http://arXiv.org/abs/1206.1244
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:17:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A hereditarily indecomposable
Banach space with rich spreading model structure" by Spiros A. Argyros
and Pavlos Motakis.
Abstract: We present a reflexive Banach space
$\mathfrak{X}_{_{^\text{usm}}}$ which is Hereditarily
Indecomposable and satisfies the following properties. In every
subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$ there exists
a weakly null normalized sequence $\{y_n\}_n$, such that every
subsymmetric sequence $\{z_n\}_n$ is isomorphically generated
as a spreading model of a subsequence of $\{y_n\}_n$. Also,
in every block subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$
there exists a seminormalized block sequence $\{z_n\}$ and
$T:\mathfrak{X}_{_{^\text{usm}}}\rightarrow\mathfrak{X}_{_{^\text{usm}}}$
an isomorphism such that for every $n\in\mathbb{N}$ $T(z_{2n-1}) =
z_{2n}$. Thus the space is an example of an HI space which is not tight
by range in a strong sense.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45
Remarks: 36 pages, no figures
Submitted from: pmotakis at central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1279
or
http://arXiv.org/abs/1206.1279
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pawel Kolwicz, Karol Lesnik, and Lech
Maligranda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:22:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Pointwise multipliers of
Calder\'on-Lozanovskii spaces" by Pawel Kolwicz, Karol Lesnik, and
Lech Maligranda.
Abstract: Several results concerning multipliers of symmetric Banach
function spaces are presented firstly. Then the results on multipliers of
Calder\'on-Lozanovskii spaces are proved. We investigate assumptions on
a Banach ideal space E and three Young functions \varphi_1, \varphi_2
and \varphi, generating the corresponding Calder\'on-Lozanovskii
spaces E_{\varphi_1}, E_{\varphi_2}, E_{\varphi} so that the space
of multipliers M(E_{\varphi_1}, E_{\varphi}) of all measurable x
such that x,y \in E_{\varphi} for any y \in E_{\varphi_1} can be
identified with E_{\varphi_2}. Sufficient conditions generalize earlier
results by Ando, O'Neil, Zabreiko-Rutickii, Maligranda-Persson and
Maligranda-Nakai. There are also necessary conditions on functions for
the embedding M(E_{\varphi_1}, E_{\varphi}) \subset E_{\varphi_2} to
be true, which already in the case when E = L^1, that is, for Orlicz
spaces M(L^{\varphi_1}, L^{\varphi}) \subset L^{\varphi_2} give a
solution of a problem raised in the book [Ma89]. Some properties of a
generalized complementary operation on Young functions, defined by Ando,
are investigated in order to show how to construct the function \varphi_2
such that M(E_{\varphi_1}, E_{\varphi}) = E_{\varphi_2}. There are also
several examples of independent interest.
Archive classification: math.FA
Mathematics Subject Classification: Functional Analysis (math.FA)
Remarks: 41 pages
Submitted from: lech.maligranda at ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1860
or
http://arXiv.org/abs/1206.1860
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gabriele Bianchi, Almut Burchard, Paolo
Gronchi, and Aljosa Volcic
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:24:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Convergence in shape of Steiner
symmetrizations" by Gabriele Bianchi, Almut Burchard, Paolo Gronchi,
and Aljosa Volcic.
Abstract: There are sequences of directions such that, given any compact
set K in R^n, the sequence of iterated Steiner symmetrals of K in these
directions converges to a ball. However examples show that Steiner
symmetrization along a sequence of directions whose differences are
square summable does not generally converge. (Note that this may happen
even with sequences of directions which are dense in S^{n-1}.) Here we
show that such sequences converge in shape. The limit need not be an
ellipsoid or even a convex set.
We also deal with uniformly distributed sequences of directions,
and with a recent result of Klain on Steiner symmetrization along
sequences chosen from a finite set of directions.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A40 (Primary) 28A75, 11K06, 26D15
(Secondary)
Remarks: 11 pages
Submitted from: gabriele.bianchi at unifi.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.2041
or
http://arXiv.org/abs/1206.2041
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dmitry V. Rutsky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 13:58:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Linear selections of superlinear
set-valued maps with some applications to analysis" by Dmitry V. Rutsky.
Abstract: A. Ya. Zaslavskii's results on the existence of a linear
(affine) selection for a linear (affine) or superlinear (convex) map
$\Phi : K \to 2^Y$ defined on a convex cone (convex set) $K$ having the
interpolation property are extended. We prove that they hold true under
more general conditions on the values of the mapping and study some other
properties of the selections. This leads to a characterization of Choquet
simplexes in terms of the existence of continuous affine selections for
arbitrary continuous convex maps. A few applications to analysis are
given, including a construction that leads to the existence of a (not
necessarily bounded) solution for the corona problem in polydisk $\mathbb
D^n$ with radial boundary values that are bounded almost everywhere on
$\mathbb T^n$.
Archive classification: math.FA
Submitted from: rutsky at pdmi.ras.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3337
or
http://arXiv.org/abs/1206.3337
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Silvia Lassalle and Martin
Mazzitelli
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 13:59:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the polynomial Lindenstrauss
theorem" by Daniel Carando, Silvia Lassalle and Martin Mazzitelli.
Abstract: Under certain hypotheses on the Banach space $X$, we show that
the set of $N$-homogeneous polynomials from $X$ to any dual space, whose
Aron-Berner extensions are norm attaining, is dense in the space of all
continuous $N$-homogeneous polynomials. To this end we prove an integral
formula for the duality between tensor products and polynomials. We
also exhibit examples of Lorentz sequence spaces for which there is
no polynomial Bishop-Phelps theorem, but our results apply. Finally
we address quantitative versions, in the sense of Bollob\'as, of these
results.
Archive classification: math.FA
Submitted from: mmazzite at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3218
or
http://arXiv.org/abs/1206.3218
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Trond A. Abrahamsen Vegard Lima, and Olav
Nygaard
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:01:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Super-ideals in Banach spaces"
by Trond A. Abrahamsen Vegard Lima, and Olav Nygaard.
Abstract: A natural class of ideals, super-ideals, of Banach spaces
is defined and studied. The motivation for working with this class of
subspaces is our observations that they inherit diameter 2 properties and
the Daugavet property. Lindenstrauss spaces are known to be the class of
Banach spaces which are ideals in every superspace; we show that being a
super-ideal in every superspace characterizes the class of Gurarii spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 14 pages
Submitted from: veli at hials.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3539
or
http://arXiv.org/abs/1206.3539
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fernando Albiac and Florent Baudier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:03:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Embeddability of snowflaked metrics
with applications to the nonlinear geometry of the spaces $L_p$ and
$\ell_{p}$ for $0<p<\infty$" by Fernando Albiac and Florent Baudier.
Abstract: We study the classical spaces $L_{p}$ and $\ell_{p}$ for the
whole range $0<p<\infty$ from a metric viewpoint and give a complete
Lipschitz embeddability roadmap between any two of those spaces when
equipped with both their ad-hoc distances and their snowflakings. Through
connections with weaker forms of embeddings that lead to basic
(yet fundamental) open problems, we also set the challenging goal
of understanding the dissimilarities between the well-known subspace
structure and the different nonlinear geometries that coexist inside
$L_{p}$ and $\ell_{p}$.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B80, 46A16, 46T99
Remarks: 25 pages
Submitted from: florent at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3774
or
http://arXiv.org/abs/1206.3774
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Barvinok
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:05:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Thrifty approximations of convex
bodies by polytopes" by Alexander Barvinok.
Abstract: Given a convex body C in R^d we construct a polytope P in C
with relatively few vertices which approximates C relatively well. In
particular, we prove that if C=-C then for any 1>epsilon>0 to have P in
C and C in (1+epsilon) P one can choose P having roughly epsilon^{-d/2}
vertices and for P in C and C in sqrt{epsilon d} P one can choose P
having roughly d^{1/epsilon} vertices. Similarly, we prove that if
C in R^d is a convex body such that -C in mu C for some mu > 1 then
to have P in C and C in (1+epsilon)P one can choose P having roughly
(mu/epsilon)^{d/2} vertices.
Archive classification: math.MG math.CO math.FA
Mathematics Subject Classification: 52A20, 52A27, 52A21, 52B55
Remarks: 13 pages
Submitted from: barvinok at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3993
or
http://arXiv.org/abs/1206.3993
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:07:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The ideal of weakly compactly
generated operators acting on a Banach space" by Tomasz Kania and Tomasz
Kochanek.
Abstract: We call a bounded linear operator acting between Banach spaces
weakly compactly generated ($\mathsf{WCG}$ for short) if its range is
contained in a weakly compactly generated subspace of its codomain. This
notion simultaneously generalises being weakly compact and having
separable range. In a comprehensive study of the class of $\mathsf{WCG}$
operators, we prove that it forms a closed surjective operator ideal
and investigate its relations to other classical operator ideals. By
considering the $p$th long James space $\mathcal{J}_p(\omega_1)$, we
show how properties of the ideal of $\mathsf{WCG}$ operators (such
as being the unique maximal ideal) may be used to derive results
outside ideal theory. For instance, we identify the $K_0$-group of
$\mathscr{B}(\mathcal{J}_p(\omega_1))$ as the additive group of integers.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary 47L10, 47L20, Secondary
46H10, 46B26
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.5424
or
http://arXiv.org/abs/1206.5424
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ivan S. Feshchenko
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:09:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On absolutely representing families
of subspaces in Banach spaces" by Ivan S. Feshchenko.
Abstract: An absolutely representing family of subspaces is a natural
generalization of an absolutely representing system of subspaces and
absolutely representing system (of elements).
We obtain necessary and (or) sufficient conditions for a family of
subspaces to be an absolutely representing family of subspaces and
study properties of absolutely representing families of subspaces in
Banach spaces. As an example, we study families of subspaces spanned
by exponents.
Archive classification: math.FA
Mathematics Subject Classification: 41A58, 46B99
Remarks: 15 pages, submitted to Vladikavkaz Mathematical Journal
Submitted from: ivanmath007 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.5496
or
http://arXiv.org/abs/1206.5496
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rui Liu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:11:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Hilbert-Schauder frame operators"
by Rui Liu.
Abstract: We introduce a new concept of frame operators for Banach spaces
we call a Hilbert-Schauder frame operator. This is a hybird between
standard frame theory for Hilbert spaces and Schauder frame theory for
Banach spaces. Most of our results involve basic structure properties
of the Hilbert-Schauder frame operator. Examples of Hilbert-Schauder
frames include standard Hilbert frames and classical bases of $\ell_p$
and $L^p$-spaces with $1< p \le 2$. Finally, we give a new isomorphic
characterization of Hilbert spaces.
Archive classification: math.FA math.CA math.OA
Mathematics Subject Classification: 46B, 47B, 47A
Remarks: 9 pages, to appear in Operators and Matrices
Submitted from: ruiliu at nankai.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.6146
or
http://arXiv.org/abs/1206.6146
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Volker Wilhelm Thurey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:20:45 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Angles and a classification of
normed spaces" by Volker Wilhelm Thurey.
Abstract: We suggest a concept of generalized `angles' in arbitrary real
normed vector spaces. We give for each real number a definition of an
`angle' by means of the shape of the unit ball. They all yield the well
known Euclidean angle in the special case of real inner product spaces.
With these different angles we achieve a classification of normed spaces,
and we obtain a characterization of inner product spaces. Finally we
consider this construction also for a generalization of normed spaces,
i.e. for spaces which may have a non-convex unit ball.
Archive classification: math.FA
Mathematics Subject Classification: 2010 AMS-classification: 46B20, 52A10
Remarks: 23 pages, 1 figure
Submitted from: volker at thuerey.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.0074
or
http://arXiv.org/abs/1207.0074
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino, Juan Seoane-Sepulveda
and Diana M. Serrano-Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:22:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "There exist multilinear
Bohnenblust--Hille constants $(C_{n})_{n=1}^{\infty}$ with $\displaystyle
\lim_{n\rightarrow \infty}(C_{n+1}-C_{n}) =0.$" by Daniel Pellegrino,
Juan Seoane-Sepulveda and Diana M. Serrano-Rodriguez.
Abstract: After almost 80 decades of dormancy, the Bohnenblust--Hille
inequalities have experienced an effervescence of new results and
sightly applications in the last years. The multilinear version of the
Bohnenblust--Hille inequality asserts that for every positive integer
$m\geq1$ there exists a sequence of positive constants $C_{m}\geq1$ such
that% \[ \left( \sum\limits_{i_{1},\ldots,i_{m}=1}^{N}\left\vert
U(e_{i_{^{1}}}% ,\ldots,e_{i_{m}})\right\vert
^{\frac{2m}{m+1}}\right) ^{\frac{m+1}{2m}}\leq
C_{m}\sup_{z_{1},\ldots,z_{m}\in\mathbb{D}^{N}}\left\vert
U(z_{1},\ldots ,z_{m})\right\vert \] for all $m$-linear forms
$U:\mathbb{C}^{N}\times\cdots\times\mathbb{C}% ^{N}\rightarrow\mathbb{C}$
and positive integers $N$ (the same holds with slightly different
constants for real scalars). The first estimates obtained for $C_{m}$
showed exponential growth but, only very recently, a striking new
panorama emerged: the polynomial Bohnenblust--Hille inequality is
hypercontractive and the multilinear Bohnenblust--Hille inequality
is subexponential. Despite all recent advances, the existence of a
family of constants $\left( C_{m}\right) _{m=1}^{\infty}$ so that \[
\lim_{n\rightarrow\infty}\left( C_{n+1}-C_{n}\right) =0 \] has not been
proved yet. The main result of this paper proves that such constants
do exist. As a consequence of this, we obtain new information on the
optimal constants $\left( K_{n}\right) _{n=1}^{\infty}$ satisfying
the multilinear Bohnenblust--Hille inequality. Let $\gamma$ be
Euler's famous constant; for any $\varepsilon>0$, we show that \[
K_{n+1}-K_{n}\leq\left( 2\sqrt{2}-4e^{\frac{1}{2}\gamma-1}\right)
n^{\log_{2}\left( 2^{-3/2}e^{1-\frac{1}{2}\gamma}\right) +\varepsilon},
\] for infinitely many $n$. Numerically, choosing a small $\varepsilon$,
\[ K_{n+1}-K_{n}\leq0.8646\left( \frac{1}{n}\right) ^{0.4737}% \] for
infinitely many $n.$
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.0124
or
http://arXiv.org/abs/1207.0124
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gustavo Garrigos, Eugenio Hernandez, and
Timur Oikhberg
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:24:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lebesgue type inequalities for
quasi-greedy bases" by Gustavo Garrigos, Eugenio Hernandez, and Timur
Oikhberg.
Abstract: We show that for quasi-greedy bases in real or complex Banach
spaces the error of the thresholding greedy algorithm of order N is
bounded by the best N- term error of approximation times a function of N
which depends on the democracy functions and the quasi-greedy constant
of the basis. If the basis is democratic this function is bounded
by C logN. We show with two examples that this bound is attained for
quasi-greedy democratic bases.
Archive classification: math.FA
Mathematics Subject Classification: 41A65, 41A46, 41A17
Report Number: 01
Remarks: 19 pages
Submitted from: eugenio.hernandez at uam.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.0946
or
http://arXiv.org/abs/1207.0946
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Lancien and Eva Pernecka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:25:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximation properties and
Schauder decompositions in Lipschitz-free spaces" by Gilles Lancien
and Eva Pernecka.
Abstract: We prove that the Lipschitz-free space over a doubling
metric space has the bounded approximation property. We also show that
the Lipschitz-free spaces over $\ell_1^N$ or $\ell_1$ have monotone
finite-dimensional Schauder decompositions.
Archive classification: math.FA
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.1583
or
http://arXiv.org/abs/1207.1583
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anil Kumar Karn and Deba Prasad Sinha
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:27:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compactness and an approximation
property related to an operator ideal" by Anil Kumar Karn and Deba
Prasad Sinha.
Abstract: For an operator ideal $\mathcal A$, we study the
composition operator ideals ${\mathcal A}\circ{\mathcal K}$, ${\mathcal
K}\circ{\mathcal A}$ and ${\mathcal K}\circ{\mathcal A}\circ{\mathcal
K}$, where $\mathcal K$ is the ideal of compact operators. We introduce
a notion of an $\mathcal A$-approximation property on a Banach space
and characterise it in terms of the density of finite rank operators in
${\mathcal A}\circ{\mathcal K}$ and ${\mathcal K}\circ{\mathcal A}$.
We propose the notions of $\ell _{\infty}$-extension and $\ell_1$-lifting
properties for an operator ideal $\mathcal A$ and study ${\mathcal
A}\circ{\mathcal K}$, ${\mathcal }\circ{\mathcal A}$ and the $\mathcal
A$-approximation property where $\mathcal A$ is injective or surjective
and/or with the $\ell _{\infty}$-extension or $\ell _1$-lifting
property. In particular, we show that if $\mathcal A$ is an injective
operator ideal with the $\ell _\infty$-extension property, then we have:
{\item{(a)} $X$ has the $\mathcal A$-approximation property if and
only if $({\mathcal A}^{min})^{inj}(Y,X)={\mathcal A}^{min}(Y,X)$,
for all Banach spaces $Y$. \item{(b)} The dual space $X^*$ has
the $\mathcal A$-approximation property if and only if $(({\mathcal
A}^{dual})^{min})^{sur}(X,Y)=({\mathcal A}^{dual})^{min}(X,Y)$, for
all Banach spaces $Y$.}For an operator ideal $\mathcal A$, we study the
composition operator ideals ${\mathcal A}\circ{\mathcal K}$,
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B50, Secondary 46B20,
46B28, 47B07
Remarks: 23 pages
Submitted from: anilkarn at niser.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.1947
or
http://arXiv.org/abs/1207.1947
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Richard Lechner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:28:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The one-third-trick and shift
operators" by Richard Lechner.
Abstract: In this paper we obtain a representation as martingale
transform operators for the rearrangement and shift operators introduced
by T. Figiel. The martingale transforms and the underlying sigma algebras
are obtained explicitly by combinatorial means. The known norm estimates
for those operators are a direct consequence of our representation.
Archive classification: math.FA
Submitted from: lechner at bayou.uni-linz.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2347
or
http://arXiv.org/abs/1207.2347
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Nunez-Alarcon and Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:30:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A simple proof that the power
$\frac{2m}{m+1}$ in the Bohnenblust--Hille inequalities is sharp" by
Daniel Nunez-Alarcon and Daniel Pellegrino.
Abstract: The power $\frac{2m}{m+1}$ in the polynomial (and multilinear)
Bohnenblust--Hille inequality is optimal. This result is well-known
but its proof highly nontrivial. In this note we present a quite simple
proof of this fact.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2662
or
http://arXiv.org/abs/1207.2662
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jose Luis Gamez-Merino and Juan B.
Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:31:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An undecidable case of lineability
in R^R" by Jose Luis Gamez-Merino and Juan B. Seoane-Sepulveda.
Abstract: Recently it has been proved that, assuming that there is an
almost disjoint family of cardinality \(2^{\mathfrak c}\) in \(\mathfrak
c\) (which is assured, for instance, by either Martin's Axiom, or CH,
or even \mbox{$2^{<\mathfrak c}=\mathfrak c$}) one has that the set of
Sierpi\'nski-Zygmund functions is \(2^{\mathfrak{c}}\)-strongly algebrable
(and, thus, \(2^{\mathfrak{c}}\)-lineable). Here we prove that these
two statements are actually equivalent and, moreover, they both are
undecidable. This would be the first time in which one encounters an
undecidable proposition in the recently coined theory of lineability.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 03E50, 03E75, 15A03, 26A15
Remarks: 5 pages
Submitted from: jseoane at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2906
or
http://arXiv.org/abs/1207.2906
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Godefroy, Gilles Lancien and Vaclav
Zizler
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:32:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The non-linear geometry of
Banach spaces after Nigel Kalton" by Gilles Godefroy, Gilles Lancien
and Vaclav Zizler.
Abstract: This is a survey of some of the results which were obtained
in the last twelve years on the non-linear geometry of Banach spaces. We
focus on the contribution of the late Nigel Kalton.
Archive classification: math.FA
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2958
or
http://arXiv.org/abs/1207.2958
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Conference honoring Prof. I Namioka
From: zpiotr at as.ysu.edu
Date: Tue, 17 Jul 2012 17:09:16 -0400 (16:09 CDT)
To: banach at math.okstate.edu
Dear Colleagues,
As you might have read in the recent notices of the AMS, we are
organizing
a Special Session "Separate versus Joint Continuity - a tribute to Prof.
I.
Namioka" during the AMS Central
Fall Sectional Meeting at the University of Akron, OH, October 20-21, 2012.
In celebration of the coming 50th anniversary of the appearance of
his
monumental "Linear topological spaces", on Friday afternoon, October 19 (a
day
before the Akron Meeting) we want to honor Prof. Namioka by slating a
mathematical gathering at Kent State University (a different location!) and
we
hope you can make it. We have contacted Prof. I. Namioka and he has kindly
agreed to give a talk at Friday's meeting.
We warmly invite you to attend these special events, both at KSU and
Akron.
We have a very limited number of slots available for a 20 minute
presentation,
so if you are interested in giving a talk/announcment please contact us
ASAP.
Regardless, whether you give a talk or not, we hope you can attend.
On behalf of the Special Session Organizing Committee
Dr. Zbigniew Piotrowski
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS-2nd announcement
From: Bill Johnson <johnson at math.tamu.edu>
Date: Wed, 25 Jul 2012 15:08:01 -0500 (CDT)
To: banach at math.okstate.edu
2nd ANNOUNCEMENT OF SUMIRFAS 2012
The Informal Regional Functional Analysis Seminar
August 3-5
Texas A&M University, College Station
Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis
and Probability page, whose NEW URL is
http://www.math.tamu.edu/~kerr/workshop/
The first talk will be in the early afternoon on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 169. The
Blocker Building is on Ireland St. just south of University Dr. on the
Texas A&M campus:
http://www.math.tamu.edu/contact/blocker.html.
Coffee and refreshments will be available in Blocker 148.
Speakers at SUMIRFAS 2012 include
Pete Casazza The Kadison-Singer Problem in Mathematics and Engineering
Ed Effros Grothendieck and Quantized Functional Analysis
Su Gao Universal equivalence relations from actions of the
unitary group
Ali Kavruk Relative Riesz Interpolations in C*-algebra Theory
Masoud Khalkhali Spectral Zeta Functions and Scalar Curvature for
Noncommutative Tori
Izabella Laba Buffon's needle estimates for rational product Cantor sets
Michael Lacey On the two weight inequality for the Hilbert transform
Paul Mueller A Davis Decomposition for Hardy Martingales
Darrin Speegle The HRT conjecture for functions with sufficiently fast
decay
Russ Thompson An introduction to the rate of escape of random walks on
groups
August 6-10 there will be a Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory",
organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and
Alexei Poltoratski. This CW is designed to bring together two groups of
experts: those specializing in complex and harmonic analysis and those
working in spectral theory of differential operators and mathematical
physics. The main goals of the CW are to study new relationships and to
widen further participation in this area in the United States.
Introductory series of lectures by Stephen Gustafson, Svetlana
Jitomirskaya, Helge Krueger, and Brett Wick are planned
to acquaint non-experts with these topics with the reasonable expectation
that some the participants in the larger Workshop will will be attracted
to this program and inject new ideas into the area.
The home page for this Workshop is at
http://www.math.tamu.edu/~comech/events/hast-2012/
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory" contact
Constanze Liaw <conni at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:05:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$\mathcal F$-bases with individual
brackets in Banach spaces" by Tomasz Kochanek.
Abstract: We provide a partial answer to the question of Vladimir Kadets
whether given an $\mathcal F$-basis of a~Banach space $X$, with respect
to some filter $\mathcal F\subset \mathcal P(\mathbb N)$, the coordinate
functionals are continuous. The answer is positive if the character of
$\mathcal F$ is less than $\mathfrak{p}$. In this case every $\mathcal
F$-basis with individual brackets is an $M$-basis with brackets determined
by a set from $\mathcal F$.
Archive classification: math.FA
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3097
or
http://arXiv.org/abs/1207.3097
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anil Kumar Karn and Deba Prasad Sinha
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:06:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An operator summability of
sequences in Banach spaces" by Anil Kumar Karn and Deba Prasad Sinha.
Abstract: Let $1 \leq p <\infty$. A sequence $\lef x_n \rig$ in a Banach
space $X$ is defined to be $p$-operator summable if for each $\lef f_n
\rig \in l^{w^*}_p(X^*)$, we have $\lef \lef f_n(x_k)\rig _k \rig _n
\in l^s_p(l_p)$. Every norm $p$-summable sequence in a Banach space is
operator $p$-summable, while in its turn every operator $p$-summable
sequence is weakly $p$-summable. An operator $T \in B(X, Y)$ is said
to be $p$-limited if for every $\lef x_n \rig \in l_p^w(X)$, $\lef Tx_n
\rig$ is operator $p$-summable. The set of all $p$-limited operators
form a normed operator ideal. It is shown that every weakly $p$-summable
sequence in $X$ is operator $p$-summable if and only if every operator
$T \in B(X, l_p)$ is $p$-absolutely summing. On the other hand every
operator $p$-summable sequence in $X$ is norm $p$-summable if and only if
every $p$-limited operator in $B(l_{p'}, X)$ is absolutely $p$-summing.
Moreover, this is the case if and only if $X$ is a subspace of $L_p(\mu )$
for some Borel measure $\mu$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B28, 46B50
Remarks: 16 pages
Submitted from: anilkarn at niser.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3620
or
http://arXiv.org/abs/1207.3620
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikolaj Krupski and Witold Marciszewski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:08:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some remarks on universality
properties of $\ell_\infty / c_0$" by Mikolaj Krupski and Witold
Marciszewski.
Abstract: We prove that if continuum is not a Kunen cardinal, then there
is a uniform Eberlein compact space $K$ such that the Banach space $C(K)$
does not embed isometrically into $\ell_\infty/c_0$. We prove a similar
result for isomorphic embeddings. We also construct a consistent example
of a uniform Eberlein compactum whose space of continuous functions
embeds isomorphically into $\ell_\infty/c_0$, but fails to embed
isometrically. As far as we know it is the first example of this kind.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B26, 46E15, Secondary 03E75
Submitted from: krupski at impan.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3722
or
http://arXiv.org/abs/1207.3722
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:10:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rigidity of commuting affine
actions on reflexive Banach spaces" by Christian Rosendal.
Abstract: We give a simple argument to show that if {\alpha} is an affine
isometric action of a product G x H of topological groups on a reflexive
Banach space X with linear part {\pi}, then either {\pi}(H) fixes a
unit vector or {\alpha}|G almost fixes a point on X. It follows that any
affine isometric action of an abelian group on a reflexive Banach space
X, whose linear part fixes no unit vectors, almost fixes points on X.
Archive classification: math.GR math.FA
Submitted from: rosendal.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3731
or
http://arXiv.org/abs/1207.3731
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Szymon Glab, Pedro L. Kaufmann and Leonardo
Pellegrini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:12:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Large structures made of
nowhere $L^p$ functions" by Szymon Glab, Pedro L. Kaufmann and Leonardo
Pellegrini.
Abstract: We say that a real-valued function $f$ defined on a
positive Borel measure space $(X,\mu)$ is nowhere $q$-integrable if,
for each nonvoid open subset $U$ of $X$, the restriction $f|_U$ is
not in $L^q(U)$. When $X$ is a Polish space and $\mu$ satisfies some
natural properties, we show that certain sets of functions which are
$p$-integrable for some $p$'s but nowhere $q$-integrable for some other
$q$'s ($0<p,q<\infty$) admit large linear and algebraic structures within
them. In our Polish space context, the presented results answer a question
from Bernal-Gonz\'alez [L. Bernal-Gonz\'alez, Algebraic genericity and
strict-order integrability, Studia Math. 199(3)(2010), 279--293], and
improves and complements results of several authors.
Archive classification: math.FA
Submitted from: leoime at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3818
or
http://arXiv.org/abs/1207.3818
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michal Kraus
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:14:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Coarse and uniform embeddings
between Orlicz sequence spaces" by Michal Kraus.
Abstract: We give an almost complete description of the coarse and
uniform embeddability between Orlicz sequence spaces. We show that
the embeddability between two Orlicz sequence spaces is in most cases
determined only by the values of their upper Matuszewska-Orlicz indices.
Archive classification: math.FA
Mathematics Subject Classification: 46B80, 46B20
Remarks: 12 pages
Submitted from: mkraus at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3967
or
http://arXiv.org/abs/1207.3967
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Peer Christian Kunstmann and Alexander
Ullmann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:16:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rs-sectorial operators and
generalized Triebel-Lizorkin spaces" by Peer Christian Kunstmann and
Alexander Ullmann.
Abstract: We introduce a notion of generalized Triebel-Lizorkin spaces
associated with sectorial operators in Banach function spaces. Our
approach is based on holomorphic functional calculus techniques. Using the
concept of $\mathcal{R}_s$-sectorial operators, which in turn is based on
the notion of $\mathcal{R}_s$-bounded sets of operators introduced by Lutz
Weis, we obtain a neat theory including equivalence of various norms and
a precise description of real and complex interpolation spaces. Another
main result of this article is that an $\mathcal{R}_s$-sectorial operator
always has a bounded $H^\infty$-functional calculus in its associated
generalized Triebel-Lizorkin spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 47A60, 47B38 (Primary), 42B25
(Secondary)
Remarks: 44 pages
Submitted from: alexander.ullmann at gmx.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4217
or
http://arXiv.org/abs/1207.4217
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Diana Ojeda-Aristizabal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:06:46 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A norm for Tsirelson's Banach
space" by Diana Ojeda-Aristizabal.
Abstract: We give an expression for the norm of the space constructed by
Tsirelson. The implicit equation satisfied by this norm is dual to the
implicit equation for the norm of the dual of Tsirelson space given by
Figiel and Johnson. The expression can be modified to give the norm of
the dual of any mixed Tsirelson space. In particular, our results can
be adapted to give the norm for the dual of Schlumprecht space.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Submitted from: dco34 at cornell.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4504
or
http://arXiv.org/abs/1207.4504
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Manor Mendel and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:08:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Nonlinear spectral calculus and
super-expanders" by Manor Mendel and Assaf Naor.
Abstract: Nonlinear spectral gaps with respect to uniformly convex
normed spaces are shown to satisfy a spectral calculus inequality that
establishes their decay along Ces\`aro averages. Nonlinear spectral
gaps of graphs are also shown to behave sub-multiplicatively under
zigzag products. These results yield a combinatorial construction of
super-expanders, i.e., a sequence of 3-regular graphs that does not
admit a coarse embedding into any uniformly convex normed space.
Archive classification: math.MG math.CO math.FA
Remarks: Some of the results of this paper were announced in
arXiv:0910.2041.
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4705
or
http://arXiv.org/abs/1207.4705
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Waleed Noor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:09:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Embeddings of M\"{u}ntz spaces:
composition operators" by S. Waleed Noor.
Abstract: Given a strictly increasing sequence $\Lambda=(\lambda_n)$
of nonegative real numbers, with $\sum_{n=1}^\infty
\frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined
as the closure in $L^p([0,1])$ of the monomials $x^{\lambda_n}$. We
discuss how properties of the embedding $M_\Lambda^2\subset L^2(\mu)$,
where $\mu$ is a finite positive Borel measure on the interval $[0,1]$,
have immediate consequences for composition operators on $M^2_\Lambda$. We
give criteria for composition operators to be bounded, compact, or to
belong to the Schatten--von Neumann ideals.
Archive classification: math.FA
Mathematics Subject Classification: 46E15, 46E20, 46E35
Citation: Integral Equations Operator Theory, Springer, 2012
Remarks: 15 Pages
Submitted from: waleed_math at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4719
or
http://arXiv.org/abs/1207.4719
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boris Rubin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:11:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Funk-Radon-Helgason
inversion method in integral geometry" by Boris Rubin.
Abstract: The paper deals with totally geodesic Radon transforms on
constant curvature spaces. We study applicability of the historically the
first Funk-Radon-Helgason method of mean value operators to reconstruction
of continuous and $L^p$ functions from their Radon transforms. New
inversion formulas involving Erd\'elyi-Kober type fractional integrals
are obtained. Particular emphasis is placed on the choice of the
differentiation operator in the spirit of the recent Helgason's formula.
Archive classification: math.FA
Mathematics Subject Classification: 44A12
Remarks: 29 pages
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.5178
or
http://arXiv.org/abs/1207.5178
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boris Rubin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:12:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Weighted norm inequalities for
k-plane transforms" by Boris Rubin.
Abstract: We obtain sharp inequalities for the k-plane transform, the
``j-plane to k-plane'' transform, and the corresponding dual transforms,
acting on $L^p$ spaces with a radial power weight. The operator
norms are
explicitly evaluated. Some generalizations and open problems are
discussed.
Archive classification: math.FA
Mathematics Subject Classification: 44A12
Remarks: 16 pages
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.5180
or
http://arXiv.org/abs/1207.5180
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas Hytonen and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:14:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Pisier's inequality revisited"
by Tuomas Hytonen and Assaf Naor.
Abstract: Given a Banach space $X$, for $n\in \mathbb N$ and $p\in
(1,\infty)$ we investigate the smallest constant $\mathfrak P\in
(0,\infty)$ for which every $f_1,\ldots,f_n:\{-1,1\}^n\to X$
satisfy \begin{multline*} \int_{\{-1,1\}^n}\Bigg\|\sum_{j=1}^n
\partial_jf_j(\varepsilon)\Bigg\|^pd\mu(\varepsilon)\\\le
\mathfrak{P}^p\int_{\{-1,1\}^n}\int_{\{-1,1\}^n}\Bigg\|\sum_{j=1}^n
\d_j\Delta f_j(\varepsilon)\Bigg\|^pd\mu(\varepsilon) d\mu(\delta),
\end{multline*} where $\mu$ is the uniform probability measure on
the discrete hypercube $\{-1,1\}^n$ and $\{\partial_j\}_{j=1}^n$ and
$\Delta=\sum_{j=1}^n\partial_j$ are the hypercube partial derivatives
and the hypercube Laplacian, respectively. Denoting this constant
by $\mathfrak{P}_p^n(X)$, we show that $\mathfrak{P}_p^n(X)\le
\sum_{k=1}^{n}\frac{1}{k}$ for every Banach space $(X,\|\cdot\|)$. This
extends the classical Pisier inequality, which corresponds to the special
case $f_j=\Delta^{-1}\partial_j f$ for some $f:\{-1,1\}^n\to X$. We show
that $\sup_{n\in \N}\mathfrak{P}_p^n(X)<\infty$ if either the dual $X^*$
is a $\mathrm{UMD}^+$ Banach space, or for some $\theta\in (0,1)$ we have
$X=[H,Y]_\theta$, where $H$ is a Hilbert space and $Y$ is an arbitrary
Banach space. It follows that $\sup_{n\in \N}\mathfrak{P}_p^n(X)<\infty$
if $X$ is a Banach lattice of finite cotype.
Archive classification: math.FA
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.5375
or
http://arXiv.org/abs/1207.5375
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Heinrich von Weizsacker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:15:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "In which spaces every curve is
Lebesgue-Pettis-integrable?" by Heinrich von Weizsacker.
Abstract: In a real locally convex Hausdorff space the closed convex
hull of every metrizable compact set is compact if (and only if)
every continuous curve has a Pettis integral with respect to Lebesgue
measure. For such spaces there is a natural concept of Bochner integrals.
Archive classification: math.FA
Mathematics Subject Classification: 46G10
Submitted from: weizsaecker at mathematik.uni-kl.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.6034
or
http://arXiv.org/abs/1207.6034
These are the messages distributed to the Banach list during 2012.
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Grzegorz Plebanek and Jose
Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:44:03 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A weak* separable C(K)* space
whose unit ball is not weak* separable" by Antonio Aviles, Grzegorz
Plebanek and Jose Rodriguez.
Abstract: We provide a ZFC example of a compact space K such that C(K)* is
w*-separable but its closed unit ball is not w*-separable. All previous
examples of such kind had been constructed under CH. We also discuss
the measurability of the supremum norm on that C(K) equipped with its
weak Baire sigma-algebra.
Archive classification: math.FA math.GN
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.5710
or
http://arXiv.org/abs/1112.5710
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by M. Jimenez-Sevilla and L. Sanchez-Gonzalez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:45:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On smooth extensions of
vector-valued functions defined on closed subsets of Banach spaces"
by M. Jimenez-Sevilla and L. Sanchez-Gonzalez.
Abstract: Let $X$ and $Z$ be Banach spaces, $A$ a closed subset of $X$
and a mapping $f:A \to Z$. We give necessary and sufficient conditions
to obtain a $C^1$ smooth mapping $F:X \to Z$ such that $F_{\mid_A}=f$,
when either (i) $X$ and $Z$ are Hilbert spaces and $X$ is separable,
or (ii) $X^*$ is separable and $Z$ is an absolute Lipschitz retract,
or (iii) $X=L_2$ and $Z=L_p$ with $1<p<2$, or (iv) $X=L_p$ and $Z=L_2$
with $2<p<\infty$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 17 pages
Submitted from: lfsanche at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.5888
or
http://arXiv.org/abs/1112.5888
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino, Joedson Santos and Juan
B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:47:49 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A general Extraplolation Theorem
for absolutely summing operators" by Daniel Pellegrino, Joedson Santos
and Juan B. Seoane-Sepulveda.
Abstract: In this note we prove a general version of the Extrapolation
Theorem, extending the classical linear extrapolation theorem due to
B. Maurey. Our result shows, in particular, that the operators involved
do not need to be linear.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.5901
or
http://arXiv.org/abs/1112.5901
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Taras Banakh, Ivan Hetman, and Katsuro
Sakai
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:51:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Recognizing the topology of the
space of closed convex subsets of a Banach space" by Taras Banakh,
Ivan Hetman, and Katsuro Sakai.
Abstract: Let $X$ be a Banach space and $Conv_H(X)$ be the space of
non-empty closed convex subsets of $X$, endowed with the Hausdorff metric
$d_H$. We prove that each connected component of the space $Conv_H(X)$ is
homeomorphic to one of the spaces: a singleton, the real line, a closed
half-plane, the Hilbert cube multiplied by the half-line, the separable
Hilbert space, or a Hilbert space of density not less than continuum.
Archive classification: math.GT math.FA math.GN math.OC
Mathematics Subject Classification: 57N20, 46A55, 46B26, 46B20, 52B05,
03E65
Remarks: 10 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.6374
or
http://arXiv.org/abs/1112.6374
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:53:45 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on the combinatorial
generation of Musielak-Orlicz spaces" by Joscha Prochno.
Abstract: We show, how one can generate Musielak-Orlicz norms, using
matrix averages and combinatorial inequalities.
Archive classification: math.FA
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0108
or
http://arXiv.org/abs/1201.0108
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Koldobsky, G. Paouris and M.
Zymonopoulou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:55:27 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Complex intersection bodies"
by A. Koldobsky, G. Paouris and M. Zymonopoulou.
Abstract: We introduce complex intersection bodies and show that
their properties and applications are similar to those of their real
counterparts. In particular, we generalize Busemann's theorem to the
complex case by proving that complex intersection bodies of symmetric
complex convex bodies are also convex. Other results include stability
in the complex Busemann-Petty problem for arbitrary measures and the
corresponding hyperplane inequality for measures of complex intersection
bodies.
Archive classification: math.FA
Submitted from: marisa.zym at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0437
or
http://arXiv.org/abs/1201.0437
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pascal Lefevre, Daniel Li, Herve Queffelec,
and Luis Rodriguez-Piazza
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 11:58:41 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some new properties of composition
operators associated with lens maps" by Pascal Lefevre, Daniel Li,
Herve Queffelec, and Luis Rodriguez-Piazza.
Abstract: We give examples of results on composition operators connected
with lens maps. The first two concern the approximation numbers of
those operators acting on the usual Hardy space $H^2$. The last ones
are connected with Hardy-Orlicz and Bergman-Orlicz spaces $H^\psi$ and
$B^\psi$, and provide a negative answer to the question of knowing if
all composition operators which are weakly compact on a non-reflexive
space are norm-compact.
Archive classification: math.FA
Remarks: 21 pages
Submitted from: daniel.li at euler.univ-artois.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0636
or
http://arXiv.org/abs/1201.0636
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas P. Hytonen and Antti V. Vahakangas
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 12:00:15 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The local non-homogeneous Tb
theorem for vector-valued functions" by Tuomas P. Hytonen and Antti
V. Vahakangas.
Abstract: We extend the local non-homogeneous Tb theorem of Nazarov, Treil
and Volberg to the setting of singular integrals with operator-valued
kernel that act on vector-valued functions. Here, `vector-valued'
means `taking values in a function lattice with the UMD (unconditional
martingale differences) property'. A similar extension (but for general
UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global
non-homogeneous Tb theorem was achieved earlier by the first author,
and it has found applications in the work of Mayboroda and Volberg on
square-functions and rectifiability. Our local version requires several
elaborations of the previous techniques, and raises new questions about
the limits of the vector-valued theory.
Archive classification: math.FA
Mathematics Subject Classification: 42B20 (Primary), 42B25, 46E40, 60G46
(Secondary)
Submitted from: antti.vahakangas at helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0648
or
http://arXiv.org/abs/1201.0648
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Godefroy and Narutaka Ozawa
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 12 Jan 2012 12:01:35 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Free Banach spaces and the
approximation properties" by Gilles Godefroy and Narutaka Ozawa.
Abstract: We characterize the metric spaces whose free space has the
bounded approximation property through a Lipschitz analogue of the local
reflexivity principle. We show that there exist compact metric spaces
whose free spaces fail the approximation property.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B28, 46B50
Remarks: 7 pages
Submitted from: narutaka at kurims.kyoto-u.ac.jp
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.0847
or
http://arXiv.org/abs/1201.0847
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Postdoctoral Fellowship in BESANCON, France
From: "Stanislaw J. Szarek" <szarek at cwru.edu>
Date: Thu, 2 Feb 2012 13:43:59 -0500 (12:43 CST)
To: banach at math.okstate.edu
Title: Postdoctoral Research Fellowship in Functional Analysis in
Besançon, France
Period: September 1, 2012 to August 31, 2013
Deadline for application: May 1, 2012.
We are now accepting applications for a postdoctoral research
fellowship (without teaching duty) for the academic year 2012-2013
(starting date: Sept. 1,2012) in the framework of the ANR project
OSQPI (Interactions between Operator Space Theory and Quantum
Probability with Applications to Quantum Information). We are looking
for applicants who received their Ph.D. recently (or will receive it
until August 2012). The fellow is expected to carry out a research
project on the topics of the ANR project OSQPI (operator spaces,
noncommutative Lp spaces, noncommutative harmonic analysis, quantum
probability, and their applications in quantum information) at the
Laboratoire de Mathématiques de Besançon (Université de
Franche-Comté). Part of the program could also be carried out at
partner institutions in Paris, Lyon, or Toulouse. The fellowship
provides a salary of about 1.800 euro per month after taxes.
For more details please contact quanhua.xu at univ-fcomte.fr
Applications should be sent to quanhua.xu at univ-fcomte.fr
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:26:57 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Absolute sums of Banach spaces
and some geometric properties related to rotundity and smoothness"
by Jan-David Hardtke.
Abstract: We study the notions of acs, luacs and uacs Banach spaces
which were introduced by V. Kadets et al. in 2000 and form common
generalisations of the usual rotundity and smoothness properties of
Banach spaces. In particular, we are interested in (mainly infinite)
absolute sums of such spaces. We also introduce some new classes of
spaces that lie inbetween those of acs and uacs spaces and study their
behaviour under taking absolute sums as well.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 42 pages, 8 figures
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.2300
or
http://arXiv.org/abs/1201.2300
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gareth Speight
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:31:46 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Surfaces meeting porous sets in
positive measure" by Gareth Speight.
Abstract: Let n>2 and X be a Banach space of dimension strictly greater
than n. We show there exists a directionally porous set P in X for which
the set of C^1 surfaces of dimension n meeting P in positive measure is
not meager. If X is separable this leads to a decomposition of X into
a countable union of directionally porous sets and a set which is null
on residually many C^1 surfaces of dimension n. This is of interest
in the study of certain classes of null sets used to investigate
differentiability of Lipschitz functions on Banach spaces.
Archive classification: math.FA math.CA math.MG
Mathematics Subject Classification: 28A75, 46T99, 46G99
Submitted from: G.Speight at Warwick.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.2376
or
http://arXiv.org/abs/1201.2376
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino and Juan B.
Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:33:41 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the hypercontractivity of the
polynomial Bohnenblust--Hille inequality" by Daniel Pellegrino and Juan
B. Seoane-Sepulveda.
Abstract: Recently, it was proved that the polynomial Bohnenblust--Hille
inequality is hypercontractive, i.e., there is a constant $C>1$
(from now on called constant of hypercontractivity) so that
$\frac{D_{m}}{D_{m-1}}=C$ for every $m$, where $D_{m}$ are constants
satisfying the polynomial Bohnenblust--Hille inequality. For the
case of multilinear mappings a recent result shows that $\lim
_{m\rightarrow\infty}\frac{C_{m}}{C_{m-1}}=1$, where $C_{m}$ are
constants satisfying the multilinear Bohnenblust--Hille inequality. So
it is natural to wonder if there exist constants $D_{m}$'s such that
$\lim_{m\rightarrow\infty}\frac{D_{m}% }{D_{m-1}}=1$. In this note we
provide lower estimates for the polynomial Bohnenblust--Hille inequality
with strong numerical evidence supporting that it is not possible to
obtain such $D_{m}.$ Besides the qualitative information, and to the
best of our knowledge, this is the first time in which non-trivial lower
bounds for the constants of the polynomial Bohnenblust--Hille inequality
are presented. We also show that the constant of hypercontractivity $C$
is so that $1.1542\leq C\leq1.8529$, providing as well explicit formulae
to improve the lower estimate $1.1542.$ It is our belief that variations
of the ideas introduced in this paper can be used for the search of the
optimal constants for the polynomial Bohnenblust--Hille inequality.
Archive classification: math.FA
Remarks: 2 figures
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.3873
or
http://arXiv.org/abs/1201.3873
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by V. Mykhaylyuk, M. Popov and B.
Randrianantoanina
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:37:27 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Enflo and narrow operators
acting on $L_p$" by V. Mykhaylyuk, M. Popov and B. Randrianantoanina.
Abstract: The paper is devoted to proofs of the following three
results. Theorem A. For $1 < p < 2$ every non-Enflo operator $T$ on $L_p$
is narrow. Theorem B. For $1 < p < 2$ every operator $T$ on $L_p$ which
is unbounded from below on $L_p(A)$, $A \subseteq [0,1]$, by means of
function having a ``gentle'' growth, is narrow. Theorem C. For $2 < p,
r < \infty$ every operator $T: L_p\rightarrow\ell_r$ is narrow.
Theorem A was mentioned by Bourgain in 1981, as a result that can
be deduced from the proof of a related result in
Johnson-Maurey-Schechtman-Tzafriri's book, but the proof from there
needed several modifications. Theorems B and C are new results. We also
discuss related open problems.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B07, secondary 47B38, 46B03
Submitted from: randrib at muohio.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.4041
or
http://arXiv.org/abs/1201.4041
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuele Casini, Enrico Miglierina, Ioannis
A. Polyrakis, and Foivos Xanthos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:44:21 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Reflexive Cones" by Emanuele
Casini, Enrico Miglierina, Ioannis A. Polyrakis, and Foivos Xanthos.
Abstract: Reflexive cones in Banach spaces are cones with weakly compact
intersection with the unit ball. In this paper we study the structure of
this class of cones. We investigate the relations between the notion of
reflexive cones and the properties of their bases. This allows us to prove
a characterization of reflexive cones in term of the absence of a subcone
isomorphic to the positive cone of \ell_{1}. Moreover, the properties
of some specific classes of reflexive cones are investigated. Namely,
we consider the reflexive cones such that the intersection with the
unit ball is norm compact, those generated by a Schauder basis and the
reflexive cones regarded as ordering cones in a Banach spaces. Finally,
it is worth to point out that a characterization of reflexive spaces and
also of the Schur spaces by the properties of reflexive cones is given.
Archive classification: math.FA
Mathematics Subject Classification: 46B10, 46B20, 46B40, 46B42
Remarks: 23 pages
Submitted from: enrico.miglierina at unicatt.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.4927
or
http://arXiv.org/abs/1201.4927
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Greg Knese
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:46:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uchiyama's lemma and the
John-Nirenberg inequality" by Greg Knese.
Abstract: Using integral formulas based on Green's theorem and in
particular a lemma of Uchiyama, we give simple proofs of comparisons of
different BMO norms without using the John-Nirenberg inequality while we
also give a simple proof of the strong John-Nirenberg inequality. Along
the way we prove the inclusions of BMOA in the dual of H^1 and BMO in
the dual of real H^1.
Archive classification: math.CV math.FA
Mathematics Subject Classification: 30H35, 30H10, 30J99
Remarks: 13 pages
Submitted from: geknese at bama.ua.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.5354
or
http://arXiv.org/abs/1201.5354
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hermann Pfitzner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:48:46 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A conjecture of Godefroy concerning
James' theorem" by Hermann Pfitzner.
Abstract: In this note we look at the interdependences between James'
theorem and the boundary problem. To do so we show a variant of James'
sup-theorem for C(K)-spaces conjectured by Godefroy: in order to know
that a bounded weakly closed subset of a C(K)- space is weakly compact
it is enough to test the sup-attainment only for measures with countable
support.
Archive classification: math.FA
Remarks: to appear in Quarterly Journal of Math.
Submitted from: Hermann.Pfitzner at univ-orleans.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1201.5471
or
http://arXiv.org/abs/1201.5471
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sebastian Scholtes
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:51:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A characterisation of inner product
spaces by the maximal circumradius of spheres" by Sebastian Scholtes.
Abstract: We will give a new characterisation of inner product spaces
amongst normed vector spaces in terms of the maximal cirumradius of
spheres. It will turn out that a normed vector space $(X,\norm{\cdot})$
with $\dim X\geq 2$ is an inner product space if and only if all spheres
are not degenerate, i.e. the maximal circumradius of points on the sphere
equals their radius.
Archive classification: math.FA math.CA math.MG
Mathematics Subject Classification: 46C15, 46B20
Remarks: 8 pages
Submitted from: sebastian.scholtes at rwth-aachen.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.0503
or
http://arXiv.org/abs/1202.0503
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by William B. Johnson, Naratuka Ozawa, and
Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:52:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A quantitative version of the
commutator theorem for zero trace matrices" by William B. Johnson,
Naratuka Ozawa, and Gideon Schechtman.
Abstract: Let $A$ be a $m\times m$ complex matrix with zero trace and
let $\e>0$. Then there are $m\times m$ matrices $B$ and $C$ such that
$A=[B,C]$ and $\|B\|\|C\|\le K_\e m^\e\|A\|$ where $K_\e$ depends only
on $\e$. Moreover, the matrix $B$ can be taken to be normal.
Archive classification: math.FA
Mathematics Subject Classification: 47B47, 15A60
Submitted from: gideon at weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.0986
or
http://arXiv.org/abs/1202.0986
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Afonso S. Bandeira, Matthew Fickus, Dustin
G. Mixon and Percy Wong
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:54:33 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The road to deterministic matrices
with the restricted isometry property" by Afonso S. Bandeira, Matthew
Fickus, Dustin G. Mixon and Percy Wong.
Abstract: The restricted isometry property (RIP) is a well-known matrix
condition that provides state-of-the-art reconstruction guarantees
for compressed sensing. While random matrices are known to satisfy
this property with high probability, deterministic constructions have
found less success. In this paper, we consider various techniques for
demonstrating RIP deterministically, some popular and some novel, and
we evaluate their performance. In evaluating some techniques, we apply
random matrix theory and inadvertently find a simple alternative proof
that certain random matrices are RIP. Later, we propose a particular class
of matrices as candidates for being RIP, namely, equiangular tight frames
(ETFs). Using the known correspondence between real ETFs and strongly
regular graphs, we investigate certain combinatorial implications of a
real ETF being RIP. Specifically, we give probabilistic intuition for
a new bound on the clique number of Paley graphs of prime order, and we
conjecture that the corresponding ETFs are RIP in a manner similar to
random matrices.
Archive classification: math.FA
Remarks: 23 pages
Submitted from: dmixon at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.1234
or
http://arXiv.org/abs/1202.1234
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kevin Beanland, Daniel Freeman, and Rui Liu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:58:13 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Upper and lower estimates for
Schauder frames and atomic decompositions" by Kevin Beanland, Daniel
Freeman, and Rui Liu.
Abstract: We prove that a Schauder frame for any separable Banach space
is shrinking if and only if it has an associated space with a shrinking
basis, and that a Schauder frame for any separable Banach space is
shrinking and boundedly complete if and only if it has a reflexive
associated space. To obtain these results, we prove that the upper and
lower estimate theorems for finite dimensional decompositions of Banach
spaces can be extended and modified to Schauder frames. We show as well
that if a separable infinite dimensional Banach space has a Schauder
frame, then it also has a Schauder frame which is not shrinking.
Archive classification: math.FA
Mathematics Subject Classification: 46B20 (Primary), 41A65 (Secondary)
Remarks: 22 pages
Submitted from: freeman at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.2492
or
http://arXiv.org/abs/1202.2492
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sean Li and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 13:59:29 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Discretization and affine
approximation in high dimensions" by Sean Li and Assaf Naor.
Abstract: Lower estimates are obtained for the macroscopic scale of
affine approximability of vector-valued Lipschitz functions on finite
dimensional normed spaces, completing the work of Bates, Johnson,
Lindenstrass, Preiss and Schechtman. This yields a new approach to
Bourgain's discretization theorem for superreflexive targets.
Archive classification: math.FA math.MG
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.2567
or
http://arXiv.org/abs/1202.2567
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cleon S. Barroso
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 16 Feb 2012 14:01:14 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the minimal space problem and
a new result on existence of basic sequences in quasi-Banach spaces"
by Cleon S. Barroso.
Abstract: We prove that if $X$ is a quasi-normed space which possesses
an infinite countable dimensional subspace with a separating dual, then
it admits a strictly weaker Hausdorff vector topology. Such a topology
is constructed explicitly. As an immediate consequence, we obtain an
improvement of a well-known result of Kalton-Shapiro and Drewnowski by
showing that a quasi-Banach space contains a basic sequence if and only
if it contains an infinite countable dimensional subspace whose dual is
separating. We also use this result to highlight a new feature of the
minimal quasi-Banach space constructed by Kalton. Namely, which all of
its $\aleph_0$-dimensional subspaces fail to have a separating family
of continuous linear functionals.
Archive classification: math.FA
Submitted from: cleonbar at mat.ufc.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.3088
or
http://arXiv.org/abs/1202.3088
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Informal Analysis Seminar at Kent State
From: Artem Zvavitch <zvavitch at math.kent.edu>
Date: Tue, 28 Feb 2012 19:42:40 -0500 (18:42 CST)
To: banach at math.okstate.edu
Dear Friends,
On March 30-April 1, 2012, the Department of Mathematical Science at
Kent State University will host famous but still very informal: INFORMAL
ANALYSIS SEMINAR and Lecture Series in Ergodic Theory and Probability.
The plan for now is to start around 3pm Friday, and finish Sunday Evening
(around 5pm). We will have lecture series by
Yuval Peres (Microsoft Research) on "Transience of random walks,
Unpredictable paths, percolation and Kakeya sets".
Mark Rudelson (University of Michigan) on "Invertibility of random
matrices".
and lectures by
Pablo Galindo (Universidad de Valencia / Purdue University), TBA
Yun Sung Choi (Postech, Pohang South Korea) on "Slicely countably
determined Banach spaces"
Miguel Martin (University of Granada) on "The Uniform Convexity, Lushness
and Bishop-Phelps-Bollobas Property"
Please, also note that on Thursday, March 29 at 4:15pm we will have a
Colloquium talk by Sergei Treil (Brown University) at 4:15.
More information can be found on
http://www.kent.edu/math/events/conferences/informal-analysis-seminar-2012.cfm
The conference fee $65, which includes pick up/drop off from the
airport/hotel and Friday/Saturday/Sunday lunches/dinners to be provided at
the department. Also, a special price of $135 has been arranged for three
nights stay at the Microtel in Streetsboro OH. The reservation must be done
through the department. If you plan to stay fewer then 3 nights or prefer
to make your own accommodation arrangements please reduce your registration
fee by $45 for each day that you will not use our hotel. If possible,
please, send a check for your registration fee, made out to "The Department
of Mathematical Sciences" to Virginia Wright, The Department of
Mathematical Sciences, Kent, State University, Kent, OH, US, 44242. The fee
can be also paid during the registration (check/cash).
Depending on availability of funds, we may waive the registration fee for
young researchers and people without available funding!!!! Please contact
Artem Zvavitch (zvavitch at math.kent.edu) or Dmitry Ryabogin
(ryabogin at math.kent.edu) as soon as possible.
SORRY FOR THE SHORT NOTICE AND LOOKING FORWARD TO SEEING YOU IN KENT!
Very Informal Analysis Group At Kent State
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Workshop at A&M
Date: Tue, 13 Mar 2012 14:29:43 -0500 (CDT)
From: Bill Johnson <johnson at math.tamu.edu>
To: banach at math.okstate.edu
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2012
The Summer 2012 Workshop in Analysis and Probability at Texas A&M
University will be in session from July 2 until August 10, 2012. For
information about the Workshop, consult the Workshop Home Page, whose NEW
URL is
http://www.math.tamu.edu/~kerr/workshop/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held
August 3-5.
July 16 - 19 there will be a Concentration Week on "Frame Theory and Maps
Between Operator Algebras",
organized by Chris Heil, Emily J. King (chair), Keri Kornelson, David
Larson (local organizer), and Darrin Speegle. A researcher working in
frame theory will naturally be led to consider matrices (the Gram matrix,
the analysis operator and the synthesis operator), and many problems in
frame theory have a re-casting in operator theory. The most celebrated
example of this is the Kadison-Singer problem. By now, there are many
mathematicians familiar with the basics of the two areas, and there is a
fruitful collaboration. Less obvious is the relationship between frame
theory and maps between operator algebras. Very recent work in this area
by Han, Larson, Lu, and Lu indicate that this may be a relationship that
is ripe for exploiting. The goal of this concentration week is to bring
together researchers in these two fields so that they may learn from one
another and build networks of potential collaborators. There will be
introductory series of talks on "Frame theory" by Ole Christensen, on
"Maps on Operator Algebras" by Vern Paulsen, and on "Bridging the Gap
Between Frame Theory and Maps on Operator Algebras" by Deguang Han. This
concentration week will also lead into a separate conference on the
following weekend celebrating the 70th birthday of David Larson. The home
page for this Workshop is at
http://page.math.tu-berlin.de/~king/cw.html
August 6-10 there will be a Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory",
organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and
Alexei Poltoratski. This CW is designed to bring together two groups of
experts: those specializing in complex and harmonic analysis and those
working in spectral theory of differential operators and mathematical
physics. The main goals of the CW are to study new relationships and to
widen further participation in this area in the United States.
Introductory series of lectures by Stephen Gustafson, Svetlana
Jitomirskaya (to be confirmed), Helge Krueger, and Brett Wick are planned
to acquaint non-experts with these topics with the reasonable expectation
that some the participants in the larger Workshop will be attracted to
this program and inject new ideas into the area.
The home page for this Workshop is at
http://www.math.tamu.edu/~comech/events/hast-2012/
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Frame Theory and Maps
Between Operator Algebras" contact Emily King <eking at math.umd.edu>
For information about the Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory" contact Constanze Liaw
<conni at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pawel Wolff
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:37:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On randomness reduction in the
Johnson-Lindenstrauss lemma" by Pawel Wolff.
Abstract: A refinement of so-called fast Johnson-Lindenstrauss
transform, due to Ailon and Chazelle (2006), and Matou\v{s}ek (2008),
is proposed. While it preserves the time efficiency and simplicity
of implementation of the original construction, it reduces randomness
used to generate the random transformation. In the analysis of the
construction two auxiliary results are established which might be
of independent interest: a Bernstein-type inequality for a sum of a
random sample from a family of independent random variables and a normal
approximation result for such a sum.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60E15, 46B85
Submitted from: pawel.wolff at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.5500
or
http://arXiv.org/abs/1202.5500
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. A. Argyros, V. Kanellopoulos, and K.
Tyros
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:42:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Higher order spreading models"
by S. A. Argyros, V. Kanellopoulos, and K. Tyros.
Abstract: We introduce the higher order spreading models associated
to a Banach space $X$. Their definition is based on $\ff$-sequences
$(x_s)_{s\in\ff}$ with $\ff$ a regular thin family and the
plegma families. We show that the higher order spreading models
of a Banach space $X$ form an increasing transfinite hierarchy
$(\mathcal{SM}_\xi(X))_{\xi<\omega_1}$. Each $\mathcal{SM}_\xi
(X)$ contains all spreading models generated by $\ff$-sequences
$(x_s)_{s\in\ff}$ with order of $\ff$ equal to $\xi$. We also provide
a study of the fundamental properties of the hierarchy.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B03, 46B06, 46B25, 46B45,
Secondary 05D10
Remarks: 37 pages
Submitted from: chcost at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.6390
or
http://arXiv.org/abs/1202.6390
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonis Manoussakis and Anna
Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:44:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strictly singular non-compact
operators on a class of HI spaces" by Antonis Manoussakis and Anna
Pelczar-Barwacz.
Abstract: We present a method for constructing bounded strictly singular
non-compact operators on mixed Tsirelson spaces defined either by the
families (A_n) or (S_n) of a certain class, as well as on spaces built
on them, including hereditarily indecomposable spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B15
Remarks: 19 pages
Submitted from: anna.pelczar at im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.0243
or
http://arXiv.org/abs/1203.0243
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gianluca Cassese
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:52:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some implications of Lebesgue
decomposition" by Gianluca Cassese.
Abstract: Based on a generalization of Lebesgue decomposition we obtain a
characterization of weak compactness in the space $ba$, a representation
of its dual space and some results on the structure of finitely additive
measures.
Archive classification: math.FA
Mathematics Subject Classification: Primary 28A25, Secondary 46B50
Submitted from: gianluca.cassese at unimib.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.1192
or
http://arXiv.org/abs/1203.1192
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sjoerd Dirksen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:54:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Noncommutative and vector-valued
Boyd interpolation theorems" by Sjoerd Dirksen.
Abstract: We present a new, elementary proof of Boyd's interpolation
theorem. Our approach naturally yields a vector-valued as well as
a noncommutative version of this result and even allows for the
interpolation of certain operators on $l^1$-valued noncommutative
symmetric spaces. By duality we may interpolate several well-known
noncommutative maximal inequalities. In particular we obtain a version of
Doob's maximal inequality and the dual Doob inequality for noncommutative
symmetric spaces. We apply our results to prove the Burkholder-Davis-Gundy
and Burkholder-Rosenthal inequalities for noncommutative martingales in
these spaces.
Archive classification: math.FA math.OA math.PR
Submitted from: sjoerd.dirksen at hcm.uni-bonn.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.1653
or
http://arXiv.org/abs/1203.1653
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Ibort, P. Linares, and J.G. Llavona
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:55:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A representation theorem
for orthogonally additive polynomials in Riesz spaces" by A. Ibort,
P. Linares, and J.G. Llavona.
Abstract: The aim of this article is to prove a representation theorem for
orthogonally additive polynomials in the spirit of the recent theorem on
representation of orthogonally additive polynomials on Banach lattices
but for the setting of Riesz spaces. To this purpose the notion of
$p$--orthosymmetric multilinear form is introduced and it is shown
to be equivalent to the or\-tho\-go\-na\-lly additive property of the
corresponding polynomial. Then the space of positive orthogonally additive
polynomials on an Archimedean Riesz space taking values on an uniformly
complete Archimedean Riesz space is shown to be isomorphic to the space
of positive linear forms on the $n$-power in the sense of Boulabiar and
Buskes of the original Riesz space.
Archive classification: math.FA
Mathematics Subject Classification: 46A40, 46G25, 47B65
Citation: Rev. Mat. Complutense, 25 (1) 21-30 (2012)
Submitted from: albertoi at math.uc3m.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.2379
or
http://arXiv.org/abs/1203.2379
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Ibort, P. Linares, and J.G. Llavona
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:57:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the representation of
orthogonally additive polynomials in $\ell_p$" by A. Ibort, P. Linares,
and J.G. Llavona.
Abstract: We present a new proof of a Sundaresan's result which shows that
the space of orthogonally additive polynomials $\mathcal{P}_o(^k\ell_p)$
is isometrically isomorphic to $\ell_{p/p-k}$ if $k<p<\infty$ and to
$\ell_\infty$ if $1\leq p\leq k$.
Archive classification: math.FA
Mathematics Subject Classification: 46G25, 46B42, 46M05
Citation: Publ. Res. Inst. Math. Sci., 45 (2) 519-24 (2009)
Submitted from: albertoi at math.uc3m.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.2968
or
http://arXiv.org/abs/1203.2968
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yang Cao, Geng Tian, and Bingzhe Hou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 09:59:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Schauder bases and operator theory"
by Yang Cao, Geng Tian, and Bingzhe Hou.
Abstract: In this paper, we firstly give a matrix approach to the bases
of a separable Hilbert space and then correct a mistake appearing in both
review and the English translation of the Olevskii's paper. After this,
we show that even a diagonal compact operator may map an orthonormal
basis into a conditional basis.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B37, 47B99, Secondary
54H20, 37B99
Remarks: 17 pages
Submitted from: caoyang at jlu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3603
or
http://arXiv.org/abs/1203.3603
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denny H. Leung and Ya-Shu Wang
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:02:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compact and weakly compact
disjointness preserving operators on spaces of differentiable functions"
by Denny H. Leung and Ya-Shu Wang.
Abstract: A pair of functions defined on a set X with values in a
vector space E is said to be disjoint if at least one of the functions
takes the value $0$ at every point in X. An operator acting between
vector-valued function spaces is disjointness preserving if it maps
disjoint functions to disjoint functions. We characterize compact and
weakly compact disjointness preserving operators between spaces of Banach
space-valued differentiable functions.
Archive classification: math.FA
Mathematics Subject Classification: 46E40, 46E50, 47B33, 47B38
Submitted from: matlhh at nus.edu.sg
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3607
or
http://arXiv.org/abs/1203.3607
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stiene Riemer and Carsten Schuett
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:04:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the expectation of the norm
of random matrices with non-identically distributed" by Stiene Riemer
and Carsten Schuett.
Abstract: We give estimates for the expectation of the norm of random
matrices with independent but not necessarily identically distributed
entries.
Archive classification: math.FA
Submitted from: riemer at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3713
or
http://arXiv.org/abs/1203.3713
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno and Stiene Riemer
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:06:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the maximum of random variables
on product spaces" by Joscha Prochno and Stiene Riemer.
Abstract: Let $\xi_i$, $i=1,...,n$, and $\eta_j$,
$j=1,...,m$ be iid p-stable respectively q-stable random
variables, $1<p<q<2$. We prove estimates for $\Ex_{\Omega_1}
\Ex_{\Omega_2}\max_{i,j}\abs{a_{ij}\xi_i(\omega_1)\eta_j(\omega_2)}$ in
terms of the $\ell_p^m(\ell_q^n)$-norm of $(a_{ij})_{i,j}$. Additionally,
for p-stable and standard gaussian random variables we prove estimates
in terms of the $\ell_p^m(\ell_{M_{\xi}}^n)$-norm, $M_{\xi}$ depending
on the Gaussians. Furthermore, we show that a sequence $\xi_i$,
$i=1,\ldots,n$ of iid $\log-\gamma(1,p)$ distributed random variables
($p\geq 2$) generates a truncated $\ell_p$-norm, especially $\Ex
\max_{i}\abs{a_i\xi_i}\sim \norm{(a_i)_i}_2$ for $p=2$. As far as we
know, the generating distribution for $\ell_p$-norms with $p\geq 2$
has not been known up to now.
Archive classification: math.FA math.PR
Remarks: 17 pages
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.3788
or
http://arXiv.org/abs/1203.3788
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jeremy Avigad and Jason Rute
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:07:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Oscillation and the mean ergodic
theorem" by Jeremy Avigad and Jason Rute.
Abstract: Let B be a uniformly convex Banach space, let T be a
nonexpansive linear operator, and let A_n x denote the ergodic average
(1/n) sum_{i<n} T^n x. A generalization of the mean ergodic theorem
due to Garrett Birkhoff asserts that the sequence (A_n x) converges,
which is equivalent to saying that for every epsilon > 0, the sequence
has only finitely many fluctuations greater than epsilon. Drawing on
calculations by Kohlenbach and Leustean, we provide a uniform bound
on the number of fluctuations that depends only on rho := || x || /
epsilon and a modulus, eta, of uniform convexity for B. Specifically,
we show that the sequence of averages (A_n x) has O(rho^2 log rho *
eta(1/(8 rho))^{-1})-many epsilon-fluctuations, and if B is a Hilbert
space, the sequence has O(rho^3 log rho)-many epsilon-fluctuations. The
proof is fully explicit, providing a remarkably uniform, quantitative,
and constructive formulation of the mean ergodic theorem.
Archive classification: math.DS math.FA math.LO
Mathematics Subject Classification: 37A30, 03F60
Submitted from: avigad at cmu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.4124
or
http://arXiv.org/abs/1203.4124
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fabio Jose Bertoloto
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 27 Mar 2012 10:10:26 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Duality of certain Banach spaces
of vector-valued holomorphic functions" by Fabio Jose Bertoloto.
Abstract: In this work we study the vector-valued Hardy spaces H p (D;
F ) (1 ≤ p ≤ ∞) and their relationship with RNP, ARNP and the UMDP
properties. By following the approach of Taylor in the scalar-valued
case, we prove that, when F and F have the ARNP property, then H p (D;
F ) and H q (D; F ) are canonically topologically isomorphic (for p,
q ∈ (1, ∞) conjugate indices) if and only if F has the UMDP.
Archive classification: math.FA
Mathematics Subject Classification: 46G20, 46G10, 30H10
Submitted from: bertoloto at famat.ufu.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.5322
or
http://arXiv.org/abs/1203.5322
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Casey Kelleher, Daniel Miller, Trenton
Osborn and Anthony Weston
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 15:56:02 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Polygonal equalities and virtual
degeneracy in $L$-spaces" by Casey Kelleher, Daniel Miller, Trenton
Osborn and Anthony Weston.
Abstract: Cases of equality in the classical $p$-negative type
inequalities for $L_{p}(\mu)$-spaces are characterized for each $p \in
(0,2)$ according to a new property called virtual degeneracy. For each
$p \in (0,2)$, this leads to a complete classification of the subsets of
$L_{p}$-spaces that have strict $p$-negative type. It follows that if $0 <
p < q \leq 2$ and if $(\Omega_{1}, \mu_{1})$ and $(\Omega_{2}, \mu_{2})$
are measure spaces, then no subset of $L_{q}(\Omega_{2}, \mu_{2})$ is
isometric to any linear subspace $W$ of $L_{p}(\Omega_{1}, \mu_{1})$
that contains a pair of disjointly supported unit vectors. Under these
circumstances it is also the case that no subset of $L_{q}(\Omega_{2},
\mu_{2})$ is isometric to any subset of $L_{p}(\Omega_{1}, \mu_{1})$
that has non-empty interior. We conclude the paper by examining virtually
degenerate subspaces of $L_{p}(\mu)$-spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Remarks: 9 pages
Submitted from: westona at canisius.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.5837
or
http://arXiv.org/abs/1203.5837
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 15:57:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Global and local boundedness of
Polish groups" by Christian Rosendal.
Abstract: We present a comprehensive theory of boundedness properties
for Polish groups developed with a main focus on Roelcke precompactness
(precompactness of the lower uniformity) and Property (OB) (boundedness of
all isometric actions on separable metric spaces). In particular, these
properties are characterised by the orbit structure of isometric actions
on metric spaces and isometric or continuous affine representations on
separable Banach spaces.
Archive classification: math.FA math.GR
Mathematics Subject Classification: Primary: 22A25, Secondary: 03E15,
46B04
Submitted from: rosendal at math.uic.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.6047
or
http://arXiv.org/abs/1203.6047
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mohammad Sadegh Asgari
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:03:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New characterizations of fusion
bases and Riesz fusion bases in hilbert spaces" by Mohammad Sadegh Asgari.
Abstract: In this paper we investigate a new notion of bases in Hilbert
spaces and similar to fusion frame theory we introduce fusion bases
theory in Hilbert spaces. We also introduce a new definition of fusion
dual sequence associated with a fusion basis and show that the operators
of a fusion dual sequence are continuous projections. Next we define
the fusion biorthogonal sequence, Bessel fusion basis, Hilbert fusion
basis and obtain some characterizations of them. we study orthonormal
fusion systems and Riesz fusion bases for Hilbert spaces. we consider the
stability of fusion bases under small perturbations. We also generalized
a result of Paley-Wiener [13] to the situation of fusion basis.
Archive classification: math.FA
Mathematics Subject Classification: Primary 42C15, Secondary 46C99
Remarks: 14 pages
Submitted from: moh.asgari at iauctb.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.6279
or
http://arXiv.org/abs/1203.6279
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eli Glasner and Michael Megrelishvili
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:05:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Banach representations and affine
compactifications of dynamical systems" by Eli Glasner and Michael
Megrelishvili.
Abstract: To every Banach space V we associate a compact right
topological affine semigroup E(V). We show that a separable Banach space
V is Asplund if and only if E(V) is metrizable, and it is Rosenthal
(i.e. it does not contain an isomorphic copy of $l_1$) if and only if
E(V) is a Rosenthal compactum. We study representations of compact right
topological semigroups in E(V). In particular, representations of tame
and HNS-semigroups arise naturally as enveloping semigroups of tame and
HNS (hereditarily non-sensitive) dynamical systems, respectively. As an
application we obtain a generalization of a theorem of R. Ellis. A main
theme of our investigation is the relationship between the enveloping
semigroup of a dynamical system X and the enveloping semigroup of its
various affine compactifications Q(X). When the two coincide we say that
the affine compactification Q(X) is E-compatible. This is a refinement of
the notion of injectivity. We show that distal non-equicontinuous systems
do not admit any E-compatible compactification. We present several new
examples of non-injective dynamical systems and examine the relationship
between injectivity and E-compatibility.
Archive classification: math.DS math.FA math.GN
Remarks: 43 pages
Submitted from: megereli at math.biu.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.0432
or
http://arXiv.org/abs/1204.0432
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Barvinok
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:07:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximations of convex bodies
by polytopes and by projections of spectrahedra" by Alexander Barvinok.
Abstract: We prove that for any compact set B in R^d and for any epsilon
>0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points
such that the maximum absolute value of any linear function ell: R^d
--> R on X approximates the maximum absolute value of ell on B within
a factor of epsilon sqrt{d}. We also prove that for any finite set B
in Z^d and for any positive integer k there is a convex set C in R^d
containing B such that C is an affine image of a section of the cone of
rxr positive semidefinite matrices for r=d^{O(k)} and such that for any
linear function ell: R^d --> R with integer coefficients the maximum
absolute value of ell on B and the maximum absolute value of ell on C
coincide provided the former does not exceed k.
Archive classification: math.MG math.FA math.OC
Mathematics Subject Classification: 52A20, 52A27, 52A21, 52B55, 90C22
Remarks: 11 pages
Submitted from: barvinok at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.0471
or
http://arXiv.org/abs/1204.0471
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rogerio Fajardo, Pedro Kaufmann and
Leonardo Pellegrini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:09:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spaceability in sets of operators
on $C(K)$" by Rogerio Fajardo, Pedro Kaufmann and Leonardo Pellegrini.
Abstract: We prove that if $K$ is a compact Hausdorff space satisfying
either condition \item $K$ contains a nontrivial convergent sequence,
or \item $C(K)$ is isomorphic to its square, then there exists an
infinite-dimensional closed subspace of the space of operators on $C(K)$,
each nonzero element of which does \emph{not} have the form $gI+S$,
where $g\in C(K)$, $S$ is weakly compact and $I$ is the identity
operator. This comes in contrast with what happens in $C(K)$ spaces
with \emph{few operators} in the sense of Koszmider [P. Koszmider,
P., Banach spaces of continuous functions with few operators. Math.
Ann. 300 (2004), no. 1, 151 - 183.], which are precisely $C(K)$ spaces
where \emph{every} operator is of the form $gI+S$.
In addition we show that, in case $C(K)$ has few operators, there is an
opertator $J$ on $C(K\times\{0,1\})=C(K)^2$ such that each operator
on $C(K\times\{0,1\})$ is of the form $gI+hJ+S$, where $g,h\in
C(K\times\{0,1\})$ and $S$ is strictly singular, in connection to a
result by Ferenczi [V. Ferenczi,Uniqueness of complex structure and
real hereditarily indecomposable Banach spaces. Adv. Math. 213 (2007),
no. 1, 462 - 488.].
Archive classification: math.FA
Submitted from: leoime at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1203.6855
or
http://arXiv.org/abs/1203.6855
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Soeren Christensen, Joscha Prochno, and
Stiene Riemer
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:13:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An inversion formula for Orlicz
norms and sequences of random variables" by Soeren Christensen, Joscha
Prochno, and Stiene Riemer.
Abstract: Given an Orlicz function $M$, we show which random variables
$\xi_i$, $i=1,...,n$ generate the associated Orlicz norm, i.e., which
random variables yield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_i\xi_i|
\sim \norm{(x_i)_{i=1}^n}_M$. As a corollary we obtain a representation
for the distribution function in terms of $M$ and $M'$ which can be
easily applied to many examples of interest.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 46B09, 60E15
Remarks: 11 pages
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.1242
or
http://arXiv.org/abs/1204.1242
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Afonso S. Bandeira, Edgar Dobriban, Dustin
G. Mixon, and William F. Sawin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:15:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Certifying the restricted isometry
property is hard" by Afonso S. Bandeira, Edgar Dobriban, Dustin G. Mixon,
and William F. Sawin.
Abstract: This paper is concerned with an important matrix condition in
compressed sensing known as the restricted isometry property (RIP). We
demonstrate that testing whether a matrix satisfies RIP is hard for
NP under randomized polynomial-time reductions. Our reduction is from
the NP-complete clique decision problem, and it uses ideas from matroid
theory. As a consequence of our result, it is impossible to efficiently
test for RIP provided NP \not\subseteq BPP, an assumption which is
slightly stronger than P \neq NP.
Archive classification: math.FA cs.IT math.IT
Remarks: 7 pages
Submitted from: dmixon at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.1580
or
http://arXiv.org/abs/1204.1580
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Geng Tian, Youqing Ji, and Yang Cao
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 25 Apr 2012 16:17:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Schauder bases and operator theory
II: (SI) Schauder operators" by Geng Tian, Youqing Ji, and Yang Cao.
Abstract: In this paper, we will show that for an operator $T$ which is
injective and has dense range, there exists an invertible operator $X$
(in fact we can find $U+K$, where $U$ is an unitary operator and $K$
is a compact operator with norm less than a given positive real number)
such that $XT$ is strongly irreducible. As its application, strongly
irreducible operators always exist in the orbit of Schauder matrices.
Archive classification: math.FA
Mathematics Subject Classification: 47A55, 47A53, 47A16, Secondary 54H20
Remarks: It is the 3rd version of our paper
Submitted from: caoyang at jlu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.1587
or
http://arXiv.org/abs/1204.1587
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Joram lindenstrauss
From: Dale Alspach <alspach at math.okstate.edu>
Date: Sun, 29 Apr 2012 14:43:24 -0500
To: banach at math.okstate.edu
Joram Lindenstrauss died today after a long illness.
His influence on Banach space theory has been enormous.
Personally, I benefited from his visits to Ohio State while I was a
graduate student and early on learned much from his books written with Lior
Tzafriri.
Dale Alspach
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean-Matthieu Auge
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:36:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Linear operators with wild
dynamics" by Jean-Matthieu Auge.
Abstract: If $X$ is a separable infinite dimensional Banach space, we
construct a bounded and linear operator $R$ on $X$ such that $$ A_R=\{x
\in X, \|R^tx\| \rightarrow \infty\} $$ is not dense and has non empty
interior with the additional property that $R$ can be written $I+K$,
where $I$ is the identity and $K$ is a compact operator. This answers
two recent questions of H\'ajek and Smith.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47A05, Secondary 47A15, 47A16
Remarks: 14 pages
Submitted from: jean-matthieu.auge at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2044
or
http://arXiv.org/abs/1204.2044
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean-Matthieu Auge
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:38:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Orbits of linear operators and
Banach space geometry" by Jean-Matthieu Auge.
Abstract: Let $T$ be a bounded linear operator on a (real or complex)
Banach space $X$. If $(a_n)$ is a sequence of non-negative numbers
tending to 0. Then, the set of $x \in X$ such that $\|T^nx\| \geqslant
a_n \|T^n\|$ for infinitely many $n$'s has a complement which is both
$\sigma$-porous and Haar-null. We also compute (for some classical
Banach space) optimal exponents $q>0$, such that for every non nilpotent
operator $T$, there exists $x \in X$ such that $(\|T^nx\|/\|T^n\|)
\notin \ell^{q}(\mathbb{N})$, using techniques which involve the modulus
of asymptotic uniform smoothness of $X$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47A05, 47A16, Secondary 28A05
Remarks: 16 pages
Submitted from: jean-matthieu.auge at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2046
or
http://arXiv.org/abs/1204.2046
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean-Matthieu Auge
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:39:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Perturbation of farthest points
in weakly compact sets" by Jean-Matthieu Auge.
Abstract: If $f$ is a real valued weakly lower semi-continous function
on a Banach space $X$ and $C$ a weakly compact subset of $X$, we show
that the set of $x \in X$ such that $z \mapsto \|x-z\|-f(z)$ attains its
supremum on $C$ is dense in $X$. We also construct a counter example
showing that the set of $x \in X$ such that $z \mapsto \|x-z\|+\|z\|$
attains its supremum on $C$ is not always dense in $X$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 41A65
Remarks: 5 pages
Submitted from: jean-matthieu.auge at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2047
or
http://arXiv.org/abs/1204.2047
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:41:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A remark on condensation of
singularities" by Jan-David Hardtke.
Abstract: Recently Alan D. Sokal gave a very short and completely
elementary proof of the uniform boundedness principle. The aim of this
note is to point out that by using a similiar technique one can give a
considerably short and simple proof of a stronger statement, namely a
principle of condensation of singularities for certain double-sequences
of non-linear operators on quasi-Banach spaces, which is a bit more
general than a result of I.\,S. G\'al.
Archive classification: math.FA
Mathematics Subject Classification: 46A16, 47H99
Remarks: 7 pages
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2106
or
http://arXiv.org/abs/1204.2106
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. Botelho, D. Cariello, V.V. Favaro, D.
Pellegrino and J.B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:43:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Subspaces
of maximal dimension contained in $L_{p}(\Omega)
- \textstyle\bigcup\limits_{q<p}L_{q}(\Omega)$}" by G. Botelho,
D. Cariello, V.V. Favaro, D. Pellegrino and J.B. Seoane-Sepulveda.
Abstract: Let $(\Omega,\Sigma,\mu)$ be a measure space and $1< p <
+\infty$. In this paper we determine when the set $L_{p}(\Omega) -
\bigcup\limits_{1 \leq q < p}L_{q}(\Omega)$ is maximal spaceable, that is,
when it contains (except for the null vector) a closed subspace $F$ of
$L_{p}(\Omega)$ such that $\dim(F) = \dim\left(L_{p}(\Omega)\right)$. The
aim of the results presented here is, among others, to generalize all the
previous work (since the 1960's) related to the linear structure of the
sets $L_{p}(\Omega) - L_{q}(\Omega)$ with $q < p$ and $L_{p}(\Omega) -
\bigcup\limits_{1 \leq q < p}L_{q}(\Omega)$. We shall also give examples,
propose open questions and provide new directions in the study of maximal
subspaces of classical measure spaces.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2170
or
http://arXiv.org/abs/1204.2170
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ronald DeVore, Guergana Petrova, and
Przemyslaw Wojtaszczyk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:44:34 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Greedy algorithms for reduced
bases in Banach spaces" by Ronald DeVore, Guergana Petrova, and Przemyslaw
Wojtaszczyk.
Abstract: Given a Banach space X and one of its compact sets F,
we consider the problem of finding a good n dimensional space X_n
⊂ X which can be used to approximate the elements of F. The best
possible error we can achieve for such an approximation is given by
the Kolmogorov width d_n(F)_X. However, finding the space which gives
this performance is typically numerically intractable. Recently, a
new greedy strategy for obtaining good spaces was given in the context
of the reduced basis method for solving a parametric family of PDEs.
The performance of this greedy algorithm was initially analyzed in
A. Buffa, Y. Maday, A.T. Patera, C. Prud’homme, and G. Turinici,
''A Priori convergence of the greedy algorithm for the parameterized
reduced basis'', M2AN Math. Model. Numer. Anal., 46(2012), 595–603 in
the case X = H is a Hilbert space. The results there were significantly
improved on in P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova,
and P. Wojtaszczyk, ''Convergence rates for greedy algorithms in reduced
bases Methods'', SIAM J. Math. Anal., 43 (2011), 1457–1472. The purpose
of the present paper is to give a new analysis of the performance of
such greedy algorithms. Our analysis not only gives improved results
for the Hilbert space case but can also be applied to the same greedy
procedure in general Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 41A46, 41A25, 46B20, 15A15
Submitted from: gpetrova at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2290
or
http://arXiv.org/abs/1204.2290
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S Dutta and A B Abubaker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:45:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Generalized 3-circular projections
in some Banach spaces" by S Dutta and A B Abubaker.
Abstract: Recently in a series of papers it is observed that in
many Banach spaces, which include classical spaces $C(\Omega)$
and $L_p$-spaces, $1 \leq p < \infty, p \neq 2$, any generalized
bi-circular projection $P$ is given by $P = \frac{I+T}{2}$, where
$I$ is the identity operator of the space and $T$ is a reflection,
that is, $T$ is a surjective isometry with $T^2 = I$. For surjective
isometries of order $n \geq 3$, the corresponding notion of projection
is generalized $n$-circular projection as defined in \cite{AD}. In this
paper we show that in a Banach space $X$, if generalized bi-circular
projections are given by $\frac{I+T}{2}$ where $T$ is a reflection,
then any generalized $n$-circular projection $P$, $n \geq 3$, is given
by $P = \frac{I+T+T^2+\cdots+T^{n-1}}{n}$ where $T$ is a surjective
isometry and $T^n = I$. We prove our results for $n=3$ and for $n > 3$,
the proof remains same except for routine modifications.
Archive classification: math.FA
Mathematics Subject Classification: 47L05, 46B20
Remarks: 8 pages
Submitted from: sudipta at iitk.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2360
or
http://arXiv.org/abs/1204.2360
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Taras Banakh, Bogdan Bokalo, and Nadiya
Kolos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:47:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On \sigma-convex subsets in spaces
of scatteredly continuous functions" by Taras Banakh, Bogdan Bokalo,
and Nadiya Kolos.
Abstract: We prove that for any topological space $X$ of countable
tightness, each \sigma-convex subspace $\F$ of the space $SC_p(X)$
of scatteredly continuous real-valued functions on $X$ has network
weight $nw(\F)\le nw(X)$. This implies that for a metrizable separable
space $X$, each compact convex subset in the function space $SC_p(X)$ is
metrizable. Another corollary says that two Tychonoff spaces $X,Y$ with
countable tightness and topologically isomorphic linear topological spaces
$SC_p(X)$ and $SC_p(Y)$ have the same network weight $nw(X)=nw(Y)$. Also
we prove that each zero-dimensional separable Rosenthal compact
space is homeomorphic to a compact subset of the function space
$SC_p(\omega^\omega)$ over the space $\omega^\omega$ of irrationals.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 46A55, 46E99, 54C35
Remarks: 6 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2438
or
http://arXiv.org/abs/1204.2438
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fedor Sukochev and Anna Tomskova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:48:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "(E,F)-multipliers and applications"
by Fedor Sukochev and Anna Tomskova.
Abstract: For two given symmetric sequence spaces $E$ and $F$ we study
the $(E,F)$-multiplier space, that is the space all of matrices $M$ for
which the Schur product $M\ast A$ maps $E$ into $F$ boundedly whenever
$A$ does. We obtain several results asserting continuous embedding of
$(E,F)$-multiplier space into the classical $(p,q)$-multiplier space
(that is when $E=l_p$, $F=l_q$). Furthermore, we present many examples
of symmetric sequence spaces $E$ and $F$ whose projective and injective
tensor products are not isomorphic to any subspace of a Banach space with
an unconditional basis, extending classical results of S. Kwapie\'{n} and
A. Pe{\l}czy\'{n}ski and of G. Bennett for the case when $E=l_p$, $F=l_q$.
Archive classification: math.FA
Remarks: 16 pages
Submitted from: tomskovaanna at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.2623
or
http://arXiv.org/abs/1204.2623
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by B. de Pagter and A.W. Wickstead
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:49:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Free and projective Banach
lattices" by B. de Pagter and A.W. Wickstead.
Abstract: We define and prove the existence of free Banach lattices in
the category of Banach lattices and contractive lattice homomorphisms and
establish some of their fundamental properties. We give much more detailed
results about their structure in the case that there are only a finite
number of generators and give several Banach lattice characterizations of
the number of generators being, respectively, one, finite or countable. We
define a Banach lattice $P$ to be projective if whenever $X$ is a Banach
lattice, $J$ a closed ideal in $X$, $Q:X\to X/J$ the quotient map,
$T:P\to X/J$ a linear lattice homomorphism and $\epsilon>0$ there is
a linear lattice homomorphism $\hat{T}:P\to X$ such that (i) $T=Q\circ
\hat{T}$ and (ii) $\|\hat{T}\|\le (1+\epsilon)\|T\|$. We establish the
connection between projective Banach lattices and free Banach lattices
and describe several families of Banach lattices that are projective as
well as proving that some are not.
Archive classification: math.FA
Submitted from: A.Wickstead at qub.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4282
or
http://arXiv.org/abs/1204.4282
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:51:26 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantification of the reciprocal
Dunford-Pettis property" by Ondrej F.K. Kalenda and Jiri Spurny.
Abstract: We prove in particular that Banach spaces of the form
$C_0(\Omega)$, where $\Omega$ is a locally compact space, enjoy a
quantitative version of the reciprocal Dunford-Pettis property.
Archive classification: math.FA
Remarks: 16 pages
Submitted from: kalenda at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4308
or
http://arXiv.org/abs/1204.4308
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Laurent W. Marcoux, Alexey I. Popov, and
Heydar Radjavi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:53:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On almost-invariant subspaces
and approximate commutation" by Laurent W. Marcoux, Alexey I. Popov,
and Heydar Radjavi.
Abstract: A closed subspace of a Banach space $\cX$ is almost-invariant
for a collection $\cS$ of bounded linear operators on $\cX$ if for each $T
\in \cS$ there exists a finite-dimensional subspace $\cF_T$ of $\cX$ such
that $T \cY \subseteq \cY + \cF_T$. In this paper, we study the existence
of almost-invariant subspaces of infinite dimension and codimension for
various classes of Banach and Hilbert space operators. We also examine
the structure of operators which admit a maximal commuting family of
almost-invariant subspaces. In particular, we prove that if $T$ is an
operator on a separable Hilbert space and if $TP-PT$ has finite rank for
all projections $P$ in a given maximal abelian self-adjoint algebra $\fM$
then $T=M+F$ where $M\in\fM$ and $F$ is of finite rank.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47A15, 47A46, 47B07, 47L10
Submitted from: a4popov at uwaterloo.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4621
or
http://arXiv.org/abs/1204.4621
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Wayne Lawton
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:55:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spectral envelopes - A preliminary
report" by Wayne Lawton.
Abstract: The spectral envelope S(F) of a subset of integers is the set
of probability measures on the circle group that are weak star limits of
squared moduli of trigonometric polynomials with frequencies in F. Fourier
transforms of these measures are positive and supported in F - F but the
converse generally fails. The characteristic function chiF of F is a
binary sequence whose orbit closure gives a symbolic dynamical system
O(F). Analytic properties of S(F) are related to dynamical properties
of chiF. The Riemann-Lebesque lemma implies that if chiF is minimal,
then S(F) is convex and hence S(F) is the closure of the convex hull of
its extreme points Se(F). In this paper we (i) review the relationship
between these concepts and the special case of the still open 1959
Kadison-Singer problem called Feichtinger's conjecture for exponential
functions, (ii) partially characterize of elements in Se(F), for minimal
chiF, in terms of ergodic properties of (O(F),lambda) where lambda is a
shift invariant probability measure whose existence in ensured by the 1937
Krylov-Bogoyubov theorem, (iii) refine previous numerical studies of the
Morse-Thue minimal binary sequence by exploiting a new MATLAB algorithm
for computing smallest eigenvalues of 4,000,000 x 4,000,000 matrices,
(iv) describe recent results characterizing S(F) for certain Bohr sets F
related to quasicrystals, (v) extend these concepts to general discrete
groups including those with Kazhdan's T-property, such as SL(n,Z), n >
2, which can be characterized by several equivalent properties such as:
any sequence of positive definite functions converging to 1 uniformly on
compact subsets converges uniformly. This exotic property may be useful
to construct a counterexample to the generalization of Feichtinger's
conjecture and hence to provide a no answer to the question of Kadison
and Singer whcih they themselves tended to suspect.
Archive classification: math.FA
Mathematics Subject Classification: 37B10, 42A55, 43A35
Remarks: To appear in Proceedings the Annual Meeting in Mathematics,
Bangkok,
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.4904
or
http://arXiv.org/abs/1204.4904
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:56:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sharp coincidences for absolutely
summing multilinear operators" by Daniel Pellegrino.
Abstract: In this note we prove the optimality of a family of known
coincidence theorems for absolutely summing multilinear operators. We
connect our results with the theory of multiple summing multilinear
operators and prove the sharpness of similar results obtained via the
complex interpolation method.
Archive classification: math.FA
Remarks: This note is part of the author's thesis which is being
written for
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.5411
or
http://arXiv.org/abs/1204.5411
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tao Mei
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 8 May 2012 13:59:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A universal $H_1$-BMO duality
theory for semigroups of operators" by Tao Mei.
Abstract: Let (M,\mu) be a sigma-finite measure space. Let (T_t)
be a semigroup of positive preserving maps on (M,\mu) with standard
assumptions. We prove a $H_1$-BMO duality theory with assumptions only
on the semigroup of operators. The H1's are defined by square functions
of P. A. Meyer's gradient form. The formulation of the assumptions does
not rely on any geometric/metric property of M nor on the kernel of the
semigroups of operators. Our main results extend to the noncommutative
setting as well, e.g. the case where $L_\infty(M,\mu)$ is replaced by
von Neuman algebras with a semifinite trace. We also prove a Carlson
embedding theorem for semigroups of operators.
Archive classification: math.CA math.FA math.OA
Mathematics Subject Classification: 46L51 42B25 46L10 47D06
Remarks: 22 pages
Submitted from: mei at wayne.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1005.4424
or
http://arXiv.org/abs/1005.4424
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. Botelho, D. Pellegrino, P. Rueda, J.
Santos and J.B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 15:56:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "When is the Haar measure a Pietsch
measure for nonlinear mappings?" by G. Botelho, D. Pellegrino, P. Rueda,
J. Santos and J.B. Seoane-Sepulveda.
Abstract: We show that, as in the linear case, the normalized Haar measure
on a compact topological group $G$ is a Pietsch measure for nonlinear
summing mappings on closed translation invariant subspaces of $C(G)$. This
answers a question posed to the authors by J. Diestel. We also show that
our result applies to several well-studied classes of nonlinear summing
mappings. In the final section some problems are proposed.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.5621
or
http://arXiv.org/abs/1204.5621
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno and Carsten Schuett
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 15:58:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Combinatorial inequalities and
subspaces of L1" by Joscha Prochno and Carsten Schuett.
Abstract: Let M and N be Orlicz functions. We establish some combinatorial
inequalities and show that the product spaces l^n_M(l^n_N) are uniformly
isomorphic to subspaces of L_1 if M and N are "separated" by a function
t^r, 1<r<2.
Archive classification: math.FA math.CO
Mathematics Subject Classification: 46B03, 05A20, 46B45, 46B09
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.6025
or
http://arXiv.org/abs/1204.6025
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 15:59:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The embedding of 2-concave
Musielak-Orlicz spaces into L_1 via l_2-matrix-averages" by Joscha
Prochno.
Abstract: In this note we prove that $\frac{1}{n!} \sum_{\pi} (
\sum_{i=1}^n |x_i a_{i,\pi(i)} |^2)^{\frac{1}{2}}$ is equivalent to a
Musielak-Orlicz norm $\norm{x}_{\sum M_i}$. We also obtain the inverse
result, i.e., given the Orlicz functions, we provide a formula for the
choice of the matrix that generates the corresponding Musielak-Orlicz
norm. As a consequence, we obtain the embedding of strictly 2-concave
Musielak-Orlicz spaces into L_1.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 05A20, 46B45
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.6030
or
http://arXiv.org/abs/1204.6030
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Szymon Glab, Pedro L. Kaufmann and Leonardo
Pellegrini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:00:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spaceability and algebrability of
sets of nowhere integrable functions" by Szymon Glab, Pedro L. Kaufmann
and Leonardo Pellegrini.
Abstract: We show that the set of Lebesgue integrable functions
in $[0,1]$ which are nowhere essentially bounded is spaceable,
improving a result from [F. J. Garc\'{i}a-Pacheco, M. Mart\'{i}n,
and J. B. Seoane-Sep\'ulveda. \textit{Lineability, spaceability,
and algebrability of certain subsets of function spaces,} Taiwanese
J. Math., \textbf{13} (2009), no. 4, 1257--1269], and that it is strongly
$\mathfrak{c}$-algebrable. We prove strong $\mathfrak{c}$-algebrability
and non-separable spaceability of the set of functions of bounded
variation which have a dense set of jump discontinuities. Applications to
sets of Lebesgue-nowhere-Riemann integrable and Riemann-nowhere-Newton
integrable functions are presented as corollaries. In addition
we prove that the set of Kurzweil integrable functions which are
not Lebesgue integrable is spaceable (in the Alexievicz norm)
but not $1$-algebrable. We also show that there exists an infinite
dimensional vector space $S$ of differentiable functions such that
each element of the $C([0,1])$-closure of $S$ is a primitive to a
Kurzweil integrable function, in connection to a classic spaceability
result from [V. I. Gurariy, \textit{Subspaces and bases in spaces of
continuous functions (Russian),} Dokl. Akad. Nauk SSSR, \textbf{167}
(1966), 971--973].
Archive classification: math.FA
Remarks: accepted on 2011
Submitted from: leoime at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1204.6404
or
http://arXiv.org/abs/1204.6404
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas P. Hytonen and Michael T. Lacey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:02:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Pointwise convergence of
vector-valued Fourier series" by Tuomas P. Hytonen and Michael T. Lacey.
Abstract: We prove a vector-valued version of Carleson's theorem:
Let Y=[X,H]_t be a complex interpolation space between a UMD space
X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the
partial sums of the Fourier series of f converge to f pointwise almost
everywhere. Apparently, all known examples of UMD spaces are of this
intermediate form Y=[X,H]_t. In particular, we answer affirmatively a
question of Rubio de Francia on the pointwise convergence of Fourier
series of Schatten class valued functions.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 42B20, 42B25
Remarks: 26 pages
Submitted from: tuomas.hytonen at helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.0261
or
http://arXiv.org/abs/1205.0261
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
Title: Estimating support functions of random polytopes via Orlicz norms
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:09:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Estimating support functions of
random polytopes via Orlicz norms" by David Alonso-Gutierrez and Joscha
Prochno.
Abstract: We study the expected value of support functions of random
polytopes in a certain direction, where the random polytope is given
by independent random vectors uniformly distributed in an isotropic
convex body. All results are obtained by an utterly novel approach,
using probabilistic estimates in connection with Orlicz norms that were
not used in this connection before.
Archive classification: math.FA
Mathematics Subject Classification: Primary 52A22, Secondary 52A23,
05D40, 46B09
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.2023
or
http://arXiv.org/abs/1205.2023
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ioannis Gasparis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:14:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A new isomorphic \ell_1 predual
not isomorphic to a complemented subspace of a C(K) space" by Ioannis
Gasparis.
Abstract: An isomorphic \(\ell_1\)-predual space \(X\) is constructed
such that neither \(X\) is isomorphic to a subspace of \(c_0\), nor
\(C(\omega^\omega)\) is isomorphic to a subspace of \(X\). It follows that
\(X\) is not isomorphic to a complemented subspace of a \(C(K)\) space.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Remarks: 12 pages
Submitted from: ioagaspa at math.auth.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/mod/1205.4317
or
http://arXiv.org/abs/mod/1205.4317
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:16:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An introduction to the Ribe
program" by Assaf Naor.
Abstract: This article accompanies the 10th Takagi Lectures, delivered
by the author at RIMS, Kyoto, on May 26 2012. It contains an exposition
of results, applications, and challenges of the Ribe program.
Archive classification: math.FA math.MG
Remarks: To appear in Japanese Journal of Mathematics
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.5993
or
http://arXiv.org/abs/1205.5993
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Jun 2012 16:17:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Gaussian behavior
of marginals and the mean width of random polytopes" by David
Alonso-Gutierrez and Joscha Prochno.
Abstract: We show that the expected value of the mean width of a random
polytope generated by $N$ random vectors ($n\leq N\leq e^{\sqrt n}$)
uniformly distributed in an isotropic convex body in $\R^n$ is of
the order $\sqrt{\log N} L_K$. This completes a result of Dafnis,
Giannopoulos and Tsolomitis. We also prove some results in connection
with the 1-dimensional marginals of the uniform probability measure on
an isotropic convex body, extending the interval in which the average
of the distribution functions of those marginals behaves in a sub-
or supergaussian way.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 52A22, 52A23, 05D40, 46B09
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.6174
or
http://arXiv.org/abs/1205.6174
Return-path: <banach-bounces at math.okstate.edu>
Subject: [Banach] SUMIRFAS announcement
From: Bill Johnson <johnson at math.tamu.edu>
Date: Thu, 21 Jun 2012 16:57:58 -0500 (CDT)
To: banach at math.okstate.edu
1st ANNOUNCEMENT OF SUMIRFAS 2012
The Informal Regional Functional Analysis Seminar
August 3-5
Texas A&M University, College Station
Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis
and Probability page, whose NEW URL is
http://www.math.tamu.edu/~kerr/workshop/
The first talk will be in the early afternoon on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 169. The
Blocker Building is on Ireland St. just south of University Dr. on the
Texas A&M campus:
http://www.math.tamu.edu/contact/blocker.html.
Coffee and refreshments will be available in Blocker 148.
Speakers at SUMIRFAS 2012 include
Pete Casazza
Ed Effros
Su Gao
Ali Kavruk
Masoud Khalkhali
Izabella Laba
Michael Lacey
Paul Mueller
Darrin Speegle
Russ Thompson
July 16 - 19 there will be a Concentration Week on "Frame Theory and Maps
Between Operator Algebras",
organized by Chris Heil, Emily J. King (chair), Keri Kornelson, and Darrin
Speegle. A researcher working in frame theory will naturally be led to
consider matrices (the Gram matrix, the analysis operator and the
synthesis operator), and many problems in frame theory have a re-casting
in operator theory. The most celebrated example of this is the
Kadison-Singer problem. By now, there are many mathematicians familiar
with the basics of the two areas, and there is a fruitful collaboration.
Less obvious is the relationship between frame theory and maps between
operator algebras. Very recent work in this area by Han, Larson, Lu, and
Lu indicate that this may be a relationship that is ripe for exploiting.
The goal of this concentration week is to bring together researchers in
these two fields so that they may learn from one another and build
networks of potential collaborators. There will be introductory series of
talks on "Frame theory" by Ole Christensen, on "Maps on Operator Algebras"
by Vern Paulsen, and on "Bridging the Gap Between Frame Theory and Maps on
Operator Algebras" by Deguang Han. This concentration week will also lead
into a separate conference on the following weekend celebrating the 70th
birthday of David Larson. The home page for this Workshop is at
http://page.math.tu-berlin.de/~king/cw.html
August 6-10 there will be a Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory",
organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and
Alexei Poltoratski. This CW is designed to bring together two groups of
experts: those specializing in complex and harmonic analysis and those
working in spectral theory of differential operators and mathematical
physics. The main goals of the CW are to study new relationships and to
widen further participation in this area in the United States.
Introductory series of lectures by Stephen Gustafson, Svetlana
Jitomirskaya, Helge Krueger, and Brett Wick are planned
to acquaint non-experts with these topics with the reasonable expectation
that some the participants in the larger Workshop will will be attracted
to this program and inject new ideas into the area.
The home page for this Workshop is at
http://www.math.tamu.edu/~comech/events/hast-2012/
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Frame Theory and Maps
Between Operator Algebras" contact Emily King <eking at math.umd.edu>
For information about the Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory" contact
Constanze Liaw <conni at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Franck Barthe, Karoly J. Boroczky, and
Matthieu Fradelizi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:12:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stability of the functional forms
of the Blaschke-Santalo inequality" by Franck Barthe, Karoly J. Boroczky,
and Matthieu Fradelizi.
Abstract: Stability versions of the functional forms of the
Blaschke-Santalo inequality due to Ball, Artstein-Klartag-Milman,
Fradelizi-Meyer and Lehec are proved.
Archive classification: math.MG math.FA
Submitted from: carlos at renyi.hu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.0369
or
http://arXiv.org/abs/1206.0369
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros, Antonis Manoussakis, and
Anna Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:13:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A type (4) space in
(FR)-classification" by Spiros A. Argyros, Antonis Manoussakis, and
Anna Pelczar-Barwacz.
Abstract: We present a reflexive Banach space with an unconditional
basis which is quasi-minimal and tight by range, i.e. of type (4) in
Ferenczi-Rosendal list within the framework of Gowers' classification
program of Banach spaces. The space is an unconditional variant of the
Gowers Hereditarily Indecomposable space with asymptotically unconditional
basis.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Remarks: 14 pages
Submitted from: anna.pelczar at im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.0651
or
http://arXiv.org/abs/1206.0651
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pierre Youssef
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:15:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Restricted Invertibility and the
Banach-Mazur distance to the cube" by Pierre Youssef.
Abstract: We prove a normalized version of the restricted invertibility
principle obtained by Spielman-Srivastava. Applying this result, we
get a new proof of the proportional Dvoretzky-Rogers factorization
theorem recovering the best current estimate. As a consequence, we
also recover the best known estimate for the Banach-Mazur distance
to the cube: the distance of every n-dimensional normed space from
\ell_{\infty }^n is at most (2n)^(5/6). Finally, using tools from the
work of Batson-Spielman-Srivastava, we give a new proof for a theorem
of Kashin-Tzafriri on the norm of restricted matrices.
Archive classification: math.FA
Submitted from: pierre.youssef at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.0654
or
http://arXiv.org/abs/1206.0654
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergey V. Astashkin, Lech Maligranda and
Konstantin E. Tikhomirov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:16:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New examples of K-monotone weighted
Banach couples" by Sergey V. Astashkin, Lech Maligranda and Konstantin
E. Tikhomirov.
Abstract: Some new examples of K-monotone couples of the type (X,
X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0,
1], are presented. Based on the property of the w-decomposability of a
symmetric space we show that, if a weight w changes sufficiently fast,
all symmetric spaces X with non-trivial Boyd indices such that the Banach
couple (X, X(w)) is K-monotone belong to the class of ultrasymmetric
Orlicz spaces. If, in addition, the fundamental function of X is t^{1/p}
for some p \in [1, \infty], then X = L_p. At the same time a Banach
couple (X, X(w)) may be K-monotone for some non-trivial w in the case
when X is not ultrasymmetric. In each of the cases where X is a Lorentz,
Marcinkiewicz or Orlicz space we have found conditions which guarantee
that (X, X(w)) is K-monotone.
Archive classification: math.FA
Mathematics Subject Classification: Functional Analysis (math.FA)
Remarks: 31 pages
Submitted from: lech.maligranda at ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1244
or
http://arXiv.org/abs/1206.1244
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:17:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A hereditarily indecomposable
Banach space with rich spreading model structure" by Spiros A. Argyros
and Pavlos Motakis.
Abstract: We present a reflexive Banach space
$\mathfrak{X}_{_{^\text{usm}}}$ which is Hereditarily
Indecomposable and satisfies the following properties. In every
subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$ there exists
a weakly null normalized sequence $\{y_n\}_n$, such that every
subsymmetric sequence $\{z_n\}_n$ is isomorphically generated
as a spreading model of a subsequence of $\{y_n\}_n$. Also,
in every block subspace $Y$ of $\mathfrak{X}_{_{^\text{usm}}}$
there exists a seminormalized block sequence $\{z_n\}$ and
$T:\mathfrak{X}_{_{^\text{usm}}}\rightarrow\mathfrak{X}_{_{^\text{usm}}}$
an isomorphism such that for every $n\in\mathbb{N}$ $T(z_{2n-1}) =
z_{2n}$. Thus the space is an example of an HI space which is not tight
by range in a strong sense.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45
Remarks: 36 pages, no figures
Submitted from: pmotakis at central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1279
or
http://arXiv.org/abs/1206.1279
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pawel Kolwicz, Karol Lesnik, and Lech
Maligranda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:22:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Pointwise multipliers of
Calder\'on-Lozanovskii spaces" by Pawel Kolwicz, Karol Lesnik, and
Lech Maligranda.
Abstract: Several results concerning multipliers of symmetric Banach
function spaces are presented firstly. Then the results on multipliers of
Calder\'on-Lozanovskii spaces are proved. We investigate assumptions on
a Banach ideal space E and three Young functions \varphi_1, \varphi_2
and \varphi, generating the corresponding Calder\'on-Lozanovskii
spaces E_{\varphi_1}, E_{\varphi_2}, E_{\varphi} so that the space
of multipliers M(E_{\varphi_1}, E_{\varphi}) of all measurable x
such that x,y \in E_{\varphi} for any y \in E_{\varphi_1} can be
identified with E_{\varphi_2}. Sufficient conditions generalize earlier
results by Ando, O'Neil, Zabreiko-Rutickii, Maligranda-Persson and
Maligranda-Nakai. There are also necessary conditions on functions for
the embedding M(E_{\varphi_1}, E_{\varphi}) \subset E_{\varphi_2} to
be true, which already in the case when E = L^1, that is, for Orlicz
spaces M(L^{\varphi_1}, L^{\varphi}) \subset L^{\varphi_2} give a
solution of a problem raised in the book [Ma89]. Some properties of a
generalized complementary operation on Young functions, defined by Ando,
are investigated in order to show how to construct the function \varphi_2
such that M(E_{\varphi_1}, E_{\varphi}) = E_{\varphi_2}. There are also
several examples of independent interest.
Archive classification: math.FA
Mathematics Subject Classification: Functional Analysis (math.FA)
Remarks: 41 pages
Submitted from: lech.maligranda at ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.1860
or
http://arXiv.org/abs/1206.1860
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gabriele Bianchi, Almut Burchard, Paolo
Gronchi, and Aljosa Volcic
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Jun 2012 16:24:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Convergence in shape of Steiner
symmetrizations" by Gabriele Bianchi, Almut Burchard, Paolo Gronchi,
and Aljosa Volcic.
Abstract: There are sequences of directions such that, given any compact
set K in R^n, the sequence of iterated Steiner symmetrals of K in these
directions converges to a ball. However examples show that Steiner
symmetrization along a sequence of directions whose differences are
square summable does not generally converge. (Note that this may happen
even with sequences of directions which are dense in S^{n-1}.) Here we
show that such sequences converge in shape. The limit need not be an
ellipsoid or even a convex set.
We also deal with uniformly distributed sequences of directions,
and with a recent result of Klain on Steiner symmetrization along
sequences chosen from a finite set of directions.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A40 (Primary) 28A75, 11K06, 26D15
(Secondary)
Remarks: 11 pages
Submitted from: gabriele.bianchi at unifi.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.2041
or
http://arXiv.org/abs/1206.2041
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dmitry V. Rutsky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 13:58:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Linear selections of superlinear
set-valued maps with some applications to analysis" by Dmitry V. Rutsky.
Abstract: A. Ya. Zaslavskii's results on the existence of a linear
(affine) selection for a linear (affine) or superlinear (convex) map
$\Phi : K \to 2^Y$ defined on a convex cone (convex set) $K$ having the
interpolation property are extended. We prove that they hold true under
more general conditions on the values of the mapping and study some other
properties of the selections. This leads to a characterization of Choquet
simplexes in terms of the existence of continuous affine selections for
arbitrary continuous convex maps. A few applications to analysis are
given, including a construction that leads to the existence of a (not
necessarily bounded) solution for the corona problem in polydisk $\mathbb
D^n$ with radial boundary values that are bounded almost everywhere on
$\mathbb T^n$.
Archive classification: math.FA
Submitted from: rutsky at pdmi.ras.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3337
or
http://arXiv.org/abs/1206.3337
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Silvia Lassalle and Martin
Mazzitelli
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 13:59:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the polynomial Lindenstrauss
theorem" by Daniel Carando, Silvia Lassalle and Martin Mazzitelli.
Abstract: Under certain hypotheses on the Banach space $X$, we show that
the set of $N$-homogeneous polynomials from $X$ to any dual space, whose
Aron-Berner extensions are norm attaining, is dense in the space of all
continuous $N$-homogeneous polynomials. To this end we prove an integral
formula for the duality between tensor products and polynomials. We
also exhibit examples of Lorentz sequence spaces for which there is
no polynomial Bishop-Phelps theorem, but our results apply. Finally
we address quantitative versions, in the sense of Bollob\'as, of these
results.
Archive classification: math.FA
Submitted from: mmazzite at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3218
or
http://arXiv.org/abs/1206.3218
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Trond A. Abrahamsen Vegard Lima, and Olav
Nygaard
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:01:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Super-ideals in Banach spaces"
by Trond A. Abrahamsen Vegard Lima, and Olav Nygaard.
Abstract: A natural class of ideals, super-ideals, of Banach spaces
is defined and studied. The motivation for working with this class of
subspaces is our observations that they inherit diameter 2 properties and
the Daugavet property. Lindenstrauss spaces are known to be the class of
Banach spaces which are ideals in every superspace; we show that being a
super-ideal in every superspace characterizes the class of Gurarii spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 14 pages
Submitted from: veli at hials.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3539
or
http://arXiv.org/abs/1206.3539
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fernando Albiac and Florent Baudier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:03:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Embeddability of snowflaked metrics
with applications to the nonlinear geometry of the spaces $L_p$ and
$\ell_{p}$ for $0<p<\infty$" by Fernando Albiac and Florent Baudier.
Abstract: We study the classical spaces $L_{p}$ and $\ell_{p}$ for the
whole range $0<p<\infty$ from a metric viewpoint and give a complete
Lipschitz embeddability roadmap between any two of those spaces when
equipped with both their ad-hoc distances and their snowflakings. Through
connections with weaker forms of embeddings that lead to basic
(yet fundamental) open problems, we also set the challenging goal
of understanding the dissimilarities between the well-known subspace
structure and the different nonlinear geometries that coexist inside
$L_{p}$ and $\ell_{p}$.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B80, 46A16, 46T99
Remarks: 25 pages
Submitted from: florent at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3774
or
http://arXiv.org/abs/1206.3774
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Barvinok
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:05:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Thrifty approximations of convex
bodies by polytopes" by Alexander Barvinok.
Abstract: Given a convex body C in R^d we construct a polytope P in C
with relatively few vertices which approximates C relatively well. In
particular, we prove that if C=-C then for any 1>epsilon>0 to have P in
C and C in (1+epsilon) P one can choose P having roughly epsilon^{-d/2}
vertices and for P in C and C in sqrt{epsilon d} P one can choose P
having roughly d^{1/epsilon} vertices. Similarly, we prove that if
C in R^d is a convex body such that -C in mu C for some mu > 1 then
to have P in C and C in (1+epsilon)P one can choose P having roughly
(mu/epsilon)^{d/2} vertices.
Archive classification: math.MG math.CO math.FA
Mathematics Subject Classification: 52A20, 52A27, 52A21, 52B55
Remarks: 13 pages
Submitted from: barvinok at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.3993
or
http://arXiv.org/abs/1206.3993
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:07:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The ideal of weakly compactly
generated operators acting on a Banach space" by Tomasz Kania and Tomasz
Kochanek.
Abstract: We call a bounded linear operator acting between Banach spaces
weakly compactly generated ($\mathsf{WCG}$ for short) if its range is
contained in a weakly compactly generated subspace of its codomain. This
notion simultaneously generalises being weakly compact and having
separable range. In a comprehensive study of the class of $\mathsf{WCG}$
operators, we prove that it forms a closed surjective operator ideal
and investigate its relations to other classical operator ideals. By
considering the $p$th long James space $\mathcal{J}_p(\omega_1)$, we
show how properties of the ideal of $\mathsf{WCG}$ operators (such
as being the unique maximal ideal) may be used to derive results
outside ideal theory. For instance, we identify the $K_0$-group of
$\mathscr{B}(\mathcal{J}_p(\omega_1))$ as the additive group of integers.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary 47L10, 47L20, Secondary
46H10, 46B26
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.5424
or
http://arXiv.org/abs/1206.5424
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ivan S. Feshchenko
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:09:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On absolutely representing families
of subspaces in Banach spaces" by Ivan S. Feshchenko.
Abstract: An absolutely representing family of subspaces is a natural
generalization of an absolutely representing system of subspaces and
absolutely representing system (of elements).
We obtain necessary and (or) sufficient conditions for a family of
subspaces to be an absolutely representing family of subspaces and
study properties of absolutely representing families of subspaces in
Banach spaces. As an example, we study families of subspaces spanned
by exponents.
Archive classification: math.FA
Mathematics Subject Classification: 41A58, 46B99
Remarks: 15 pages, submitted to Vladikavkaz Mathematical Journal
Submitted from: ivanmath007 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.5496
or
http://arXiv.org/abs/1206.5496
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rui Liu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 28 Jun 2012 14:11:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Hilbert-Schauder frame operators"
by Rui Liu.
Abstract: We introduce a new concept of frame operators for Banach spaces
we call a Hilbert-Schauder frame operator. This is a hybird between
standard frame theory for Hilbert spaces and Schauder frame theory for
Banach spaces. Most of our results involve basic structure properties
of the Hilbert-Schauder frame operator. Examples of Hilbert-Schauder
frames include standard Hilbert frames and classical bases of $\ell_p$
and $L^p$-spaces with $1< p \le 2$. Finally, we give a new isomorphic
characterization of Hilbert spaces.
Archive classification: math.FA math.CA math.OA
Mathematics Subject Classification: 46B, 47B, 47A
Remarks: 9 pages, to appear in Operators and Matrices
Submitted from: ruiliu at nankai.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1206.6146
or
http://arXiv.org/abs/1206.6146
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Volker Wilhelm Thurey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:20:45 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Angles and a classification of
normed spaces" by Volker Wilhelm Thurey.
Abstract: We suggest a concept of generalized `angles' in arbitrary real
normed vector spaces. We give for each real number a definition of an
`angle' by means of the shape of the unit ball. They all yield the well
known Euclidean angle in the special case of real inner product spaces.
With these different angles we achieve a classification of normed spaces,
and we obtain a characterization of inner product spaces. Finally we
consider this construction also for a generalization of normed spaces,
i.e. for spaces which may have a non-convex unit ball.
Archive classification: math.FA
Mathematics Subject Classification: 2010 AMS-classification: 46B20, 52A10
Remarks: 23 pages, 1 figure
Submitted from: volker at thuerey.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.0074
or
http://arXiv.org/abs/1207.0074
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino, Juan Seoane-Sepulveda
and Diana M. Serrano-Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:22:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "There exist multilinear
Bohnenblust--Hille constants $(C_{n})_{n=1}^{\infty}$ with $\displaystyle
\lim_{n\rightarrow \infty}(C_{n+1}-C_{n}) =0.$" by Daniel Pellegrino,
Juan Seoane-Sepulveda and Diana M. Serrano-Rodriguez.
Abstract: After almost 80 decades of dormancy, the Bohnenblust--Hille
inequalities have experienced an effervescence of new results and
sightly applications in the last years. The multilinear version of the
Bohnenblust--Hille inequality asserts that for every positive integer
$m\geq1$ there exists a sequence of positive constants $C_{m}\geq1$ such
that% \[ \left( \sum\limits_{i_{1},\ldots,i_{m}=1}^{N}\left\vert
U(e_{i_{^{1}}}% ,\ldots,e_{i_{m}})\right\vert
^{\frac{2m}{m+1}}\right) ^{\frac{m+1}{2m}}\leq
C_{m}\sup_{z_{1},\ldots,z_{m}\in\mathbb{D}^{N}}\left\vert
U(z_{1},\ldots ,z_{m})\right\vert \] for all $m$-linear forms
$U:\mathbb{C}^{N}\times\cdots\times\mathbb{C}% ^{N}\rightarrow\mathbb{C}$
and positive integers $N$ (the same holds with slightly different
constants for real scalars). The first estimates obtained for $C_{m}$
showed exponential growth but, only very recently, a striking new
panorama emerged: the polynomial Bohnenblust--Hille inequality is
hypercontractive and the multilinear Bohnenblust--Hille inequality
is subexponential. Despite all recent advances, the existence of a
family of constants $\left( C_{m}\right) _{m=1}^{\infty}$ so that \[
\lim_{n\rightarrow\infty}\left( C_{n+1}-C_{n}\right) =0 \] has not been
proved yet. The main result of this paper proves that such constants
do exist. As a consequence of this, we obtain new information on the
optimal constants $\left( K_{n}\right) _{n=1}^{\infty}$ satisfying
the multilinear Bohnenblust--Hille inequality. Let $\gamma$ be
Euler's famous constant; for any $\varepsilon>0$, we show that \[
K_{n+1}-K_{n}\leq\left( 2\sqrt{2}-4e^{\frac{1}{2}\gamma-1}\right)
n^{\log_{2}\left( 2^{-3/2}e^{1-\frac{1}{2}\gamma}\right) +\varepsilon},
\] for infinitely many $n$. Numerically, choosing a small $\varepsilon$,
\[ K_{n+1}-K_{n}\leq0.8646\left( \frac{1}{n}\right) ^{0.4737}% \] for
infinitely many $n.$
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.0124
or
http://arXiv.org/abs/1207.0124
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gustavo Garrigos, Eugenio Hernandez, and
Timur Oikhberg
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:24:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lebesgue type inequalities for
quasi-greedy bases" by Gustavo Garrigos, Eugenio Hernandez, and Timur
Oikhberg.
Abstract: We show that for quasi-greedy bases in real or complex Banach
spaces the error of the thresholding greedy algorithm of order N is
bounded by the best N- term error of approximation times a function of N
which depends on the democracy functions and the quasi-greedy constant
of the basis. If the basis is democratic this function is bounded
by C logN. We show with two examples that this bound is attained for
quasi-greedy democratic bases.
Archive classification: math.FA
Mathematics Subject Classification: 41A65, 41A46, 41A17
Report Number: 01
Remarks: 19 pages
Submitted from: eugenio.hernandez at uam.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.0946
or
http://arXiv.org/abs/1207.0946
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Lancien and Eva Pernecka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:25:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximation properties and
Schauder decompositions in Lipschitz-free spaces" by Gilles Lancien
and Eva Pernecka.
Abstract: We prove that the Lipschitz-free space over a doubling
metric space has the bounded approximation property. We also show that
the Lipschitz-free spaces over $\ell_1^N$ or $\ell_1$ have monotone
finite-dimensional Schauder decompositions.
Archive classification: math.FA
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.1583
or
http://arXiv.org/abs/1207.1583
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anil Kumar Karn and Deba Prasad Sinha
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:27:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compactness and an approximation
property related to an operator ideal" by Anil Kumar Karn and Deba
Prasad Sinha.
Abstract: For an operator ideal $\mathcal A$, we study the
composition operator ideals ${\mathcal A}\circ{\mathcal K}$, ${\mathcal
K}\circ{\mathcal A}$ and ${\mathcal K}\circ{\mathcal A}\circ{\mathcal
K}$, where $\mathcal K$ is the ideal of compact operators. We introduce
a notion of an $\mathcal A$-approximation property on a Banach space
and characterise it in terms of the density of finite rank operators in
${\mathcal A}\circ{\mathcal K}$ and ${\mathcal K}\circ{\mathcal A}$.
We propose the notions of $\ell _{\infty}$-extension and $\ell_1$-lifting
properties for an operator ideal $\mathcal A$ and study ${\mathcal
A}\circ{\mathcal K}$, ${\mathcal }\circ{\mathcal A}$ and the $\mathcal
A$-approximation property where $\mathcal A$ is injective or surjective
and/or with the $\ell _{\infty}$-extension or $\ell _1$-lifting
property. In particular, we show that if $\mathcal A$ is an injective
operator ideal with the $\ell _\infty$-extension property, then we have:
{\item{(a)} $X$ has the $\mathcal A$-approximation property if and
only if $({\mathcal A}^{min})^{inj}(Y,X)={\mathcal A}^{min}(Y,X)$,
for all Banach spaces $Y$. \item{(b)} The dual space $X^*$ has
the $\mathcal A$-approximation property if and only if $(({\mathcal
A}^{dual})^{min})^{sur}(X,Y)=({\mathcal A}^{dual})^{min}(X,Y)$, for
all Banach spaces $Y$.}For an operator ideal $\mathcal A$, we study the
composition operator ideals ${\mathcal A}\circ{\mathcal K}$,
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B50, Secondary 46B20,
46B28, 47B07
Remarks: 23 pages
Submitted from: anilkarn at niser.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.1947
or
http://arXiv.org/abs/1207.1947
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Richard Lechner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:28:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The one-third-trick and shift
operators" by Richard Lechner.
Abstract: In this paper we obtain a representation as martingale
transform operators for the rearrangement and shift operators introduced
by T. Figiel. The martingale transforms and the underlying sigma algebras
are obtained explicitly by combinatorial means. The known norm estimates
for those operators are a direct consequence of our representation.
Archive classification: math.FA
Submitted from: lechner at bayou.uni-linz.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2347
or
http://arXiv.org/abs/1207.2347
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Nunez-Alarcon and Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:30:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A simple proof that the power
$\frac{2m}{m+1}$ in the Bohnenblust--Hille inequalities is sharp" by
Daniel Nunez-Alarcon and Daniel Pellegrino.
Abstract: The power $\frac{2m}{m+1}$ in the polynomial (and multilinear)
Bohnenblust--Hille inequality is optimal. This result is well-known
but its proof highly nontrivial. In this note we present a quite simple
proof of this fact.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2662
or
http://arXiv.org/abs/1207.2662
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jose Luis Gamez-Merino and Juan B.
Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:31:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An undecidable case of lineability
in R^R" by Jose Luis Gamez-Merino and Juan B. Seoane-Sepulveda.
Abstract: Recently it has been proved that, assuming that there is an
almost disjoint family of cardinality \(2^{\mathfrak c}\) in \(\mathfrak
c\) (which is assured, for instance, by either Martin's Axiom, or CH,
or even \mbox{$2^{<\mathfrak c}=\mathfrak c$}) one has that the set of
Sierpi\'nski-Zygmund functions is \(2^{\mathfrak{c}}\)-strongly algebrable
(and, thus, \(2^{\mathfrak{c}}\)-lineable). Here we prove that these
two statements are actually equivalent and, moreover, they both are
undecidable. This would be the first time in which one encounters an
undecidable proposition in the recently coined theory of lineability.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 03E50, 03E75, 15A03, 26A15
Remarks: 5 pages
Submitted from: jseoane at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2906
or
http://arXiv.org/abs/1207.2906
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Godefroy, Gilles Lancien and Vaclav
Zizler
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 Jul 2012 12:32:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The non-linear geometry of
Banach spaces after Nigel Kalton" by Gilles Godefroy, Gilles Lancien
and Vaclav Zizler.
Abstract: This is a survey of some of the results which were obtained
in the last twelve years on the non-linear geometry of Banach spaces. We
focus on the contribution of the late Nigel Kalton.
Archive classification: math.FA
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.2958
or
http://arXiv.org/abs/1207.2958
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Conference honoring Prof. I Namioka
From: zpiotr at as.ysu.edu
Date: Tue, 17 Jul 2012 17:09:16 -0400 (16:09 CDT)
To: banach at math.okstate.edu
Dear Colleagues,
As you might have read in the recent notices of the AMS, we are
organizing
a Special Session "Separate versus Joint Continuity - a tribute to Prof.
I.
Namioka" during the AMS Central
Fall Sectional Meeting at the University of Akron, OH, October 20-21, 2012.
In celebration of the coming 50th anniversary of the appearance of
his
monumental "Linear topological spaces", on Friday afternoon, October 19 (a
day
before the Akron Meeting) we want to honor Prof. Namioka by slating a
mathematical gathering at Kent State University (a different location!) and
we
hope you can make it. We have contacted Prof. I. Namioka and he has kindly
agreed to give a talk at Friday's meeting.
We warmly invite you to attend these special events, both at KSU and
Akron.
We have a very limited number of slots available for a 20 minute
presentation,
so if you are interested in giving a talk/announcment please contact us
ASAP.
Regardless, whether you give a talk or not, we hope you can attend.
On behalf of the Special Session Organizing Committee
Dr. Zbigniew Piotrowski
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS-2nd announcement
From: Bill Johnson <johnson at math.tamu.edu>
Date: Wed, 25 Jul 2012 15:08:01 -0500 (CDT)
To: banach at math.okstate.edu
2nd ANNOUNCEMENT OF SUMIRFAS 2012
The Informal Regional Functional Analysis Seminar
August 3-5
Texas A&M University, College Station
Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis
and Probability page, whose NEW URL is
http://www.math.tamu.edu/~kerr/workshop/
The first talk will be in the early afternoon on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 169. The
Blocker Building is on Ireland St. just south of University Dr. on the
Texas A&M campus:
http://www.math.tamu.edu/contact/blocker.html.
Coffee and refreshments will be available in Blocker 148.
Speakers at SUMIRFAS 2012 include
Pete Casazza The Kadison-Singer Problem in Mathematics and Engineering
Ed Effros Grothendieck and Quantized Functional Analysis
Su Gao Universal equivalence relations from actions of the
unitary group
Ali Kavruk Relative Riesz Interpolations in C*-algebra Theory
Masoud Khalkhali Spectral Zeta Functions and Scalar Curvature for
Noncommutative Tori
Izabella Laba Buffon's needle estimates for rational product Cantor sets
Michael Lacey On the two weight inequality for the Hilbert transform
Paul Mueller A Davis Decomposition for Hardy Martingales
Darrin Speegle The HRT conjecture for functions with sufficiently fast
decay
Russ Thompson An introduction to the rate of escape of random walks on
groups
August 6-10 there will be a Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory",
organized by Andrew Comech, David Damanik, Constanze Liaw (chair), and
Alexei Poltoratski. This CW is designed to bring together two groups of
experts: those specializing in complex and harmonic analysis and those
working in spectral theory of differential operators and mathematical
physics. The main goals of the CW are to study new relationships and to
widen further participation in this area in the United States.
Introductory series of lectures by Stephen Gustafson, Svetlana
Jitomirskaya, Helge Krueger, and Brett Wick are planned
to acquaint non-experts with these topics with the reasonable expectation
that some the participants in the larger Workshop will will be attracted
to this program and inject new ideas into the area.
The home page for this Workshop is at
http://www.math.tamu.edu/~comech/events/hast-2012/
The Workshop is supported in part by grants from the National Science
Foundation (NSF). Minorities, women, graduate students, and young
researchers are especially encouraged to attend.
For logistical support, including requests for support, please contact
Cara Barton <cara at math.tamu.edu>. For more information on the Workshop
itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr
<kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>.
For information about the Concentration Week on "Recent advances in
Harmonic Analysis and Spectral Theory" contact
Constanze Liaw <conni at math.tamu.edu>
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:05:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$\mathcal F$-bases with individual
brackets in Banach spaces" by Tomasz Kochanek.
Abstract: We provide a partial answer to the question of Vladimir Kadets
whether given an $\mathcal F$-basis of a~Banach space $X$, with respect
to some filter $\mathcal F\subset \mathcal P(\mathbb N)$, the coordinate
functionals are continuous. The answer is positive if the character of
$\mathcal F$ is less than $\mathfrak{p}$. In this case every $\mathcal
F$-basis with individual brackets is an $M$-basis with brackets determined
by a set from $\mathcal F$.
Archive classification: math.FA
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3097
or
http://arXiv.org/abs/1207.3097
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anil Kumar Karn and Deba Prasad Sinha
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:06:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An operator summability of
sequences in Banach spaces" by Anil Kumar Karn and Deba Prasad Sinha.
Abstract: Let $1 \leq p <\infty$. A sequence $\lef x_n \rig$ in a Banach
space $X$ is defined to be $p$-operator summable if for each $\lef f_n
\rig \in l^{w^*}_p(X^*)$, we have $\lef \lef f_n(x_k)\rig _k \rig _n
\in l^s_p(l_p)$. Every norm $p$-summable sequence in a Banach space is
operator $p$-summable, while in its turn every operator $p$-summable
sequence is weakly $p$-summable. An operator $T \in B(X, Y)$ is said
to be $p$-limited if for every $\lef x_n \rig \in l_p^w(X)$, $\lef Tx_n
\rig$ is operator $p$-summable. The set of all $p$-limited operators
form a normed operator ideal. It is shown that every weakly $p$-summable
sequence in $X$ is operator $p$-summable if and only if every operator
$T \in B(X, l_p)$ is $p$-absolutely summing. On the other hand every
operator $p$-summable sequence in $X$ is norm $p$-summable if and only if
every $p$-limited operator in $B(l_{p'}, X)$ is absolutely $p$-summing.
Moreover, this is the case if and only if $X$ is a subspace of $L_p(\mu )$
for some Borel measure $\mu$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B28, 46B50
Remarks: 16 pages
Submitted from: anilkarn at niser.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3620
or
http://arXiv.org/abs/1207.3620
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikolaj Krupski and Witold Marciszewski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:08:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some remarks on universality
properties of $\ell_\infty / c_0$" by Mikolaj Krupski and Witold
Marciszewski.
Abstract: We prove that if continuum is not a Kunen cardinal, then there
is a uniform Eberlein compact space $K$ such that the Banach space $C(K)$
does not embed isometrically into $\ell_\infty/c_0$. We prove a similar
result for isomorphic embeddings. We also construct a consistent example
of a uniform Eberlein compactum whose space of continuous functions
embeds isomorphically into $\ell_\infty/c_0$, but fails to embed
isometrically. As far as we know it is the first example of this kind.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B26, 46E15, Secondary 03E75
Submitted from: krupski at impan.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3722
or
http://arXiv.org/abs/1207.3722
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:10:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rigidity of commuting affine
actions on reflexive Banach spaces" by Christian Rosendal.
Abstract: We give a simple argument to show that if {\alpha} is an affine
isometric action of a product G x H of topological groups on a reflexive
Banach space X with linear part {\pi}, then either {\pi}(H) fixes a
unit vector or {\alpha}|G almost fixes a point on X. It follows that any
affine isometric action of an abelian group on a reflexive Banach space
X, whose linear part fixes no unit vectors, almost fixes points on X.
Archive classification: math.GR math.FA
Submitted from: rosendal.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3731
or
http://arXiv.org/abs/1207.3731
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Szymon Glab, Pedro L. Kaufmann and Leonardo
Pellegrini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:12:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Large structures made of
nowhere $L^p$ functions" by Szymon Glab, Pedro L. Kaufmann and Leonardo
Pellegrini.
Abstract: We say that a real-valued function $f$ defined on a
positive Borel measure space $(X,\mu)$ is nowhere $q$-integrable if,
for each nonvoid open subset $U$ of $X$, the restriction $f|_U$ is
not in $L^q(U)$. When $X$ is a Polish space and $\mu$ satisfies some
natural properties, we show that certain sets of functions which are
$p$-integrable for some $p$'s but nowhere $q$-integrable for some other
$q$'s ($0<p,q<\infty$) admit large linear and algebraic structures within
them. In our Polish space context, the presented results answer a question
from Bernal-Gonz\'alez [L. Bernal-Gonz\'alez, Algebraic genericity and
strict-order integrability, Studia Math. 199(3)(2010), 279--293], and
improves and complements results of several authors.
Archive classification: math.FA
Submitted from: leoime at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3818
or
http://arXiv.org/abs/1207.3818
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michal Kraus
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:14:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Coarse and uniform embeddings
between Orlicz sequence spaces" by Michal Kraus.
Abstract: We give an almost complete description of the coarse and
uniform embeddability between Orlicz sequence spaces. We show that
the embeddability between two Orlicz sequence spaces is in most cases
determined only by the values of their upper Matuszewska-Orlicz indices.
Archive classification: math.FA
Mathematics Subject Classification: 46B80, 46B20
Remarks: 12 pages
Submitted from: mkraus at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.3967
or
http://arXiv.org/abs/1207.3967
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Peer Christian Kunstmann and Alexander
Ullmann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 11:16:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rs-sectorial operators and
generalized Triebel-Lizorkin spaces" by Peer Christian Kunstmann and
Alexander Ullmann.
Abstract: We introduce a notion of generalized Triebel-Lizorkin spaces
associated with sectorial operators in Banach function spaces. Our
approach is based on holomorphic functional calculus techniques. Using the
concept of $\mathcal{R}_s$-sectorial operators, which in turn is based on
the notion of $\mathcal{R}_s$-bounded sets of operators introduced by Lutz
Weis, we obtain a neat theory including equivalence of various norms and
a precise description of real and complex interpolation spaces. Another
main result of this article is that an $\mathcal{R}_s$-sectorial operator
always has a bounded $H^\infty$-functional calculus in its associated
generalized Triebel-Lizorkin spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 47A60, 47B38 (Primary), 42B25
(Secondary)
Remarks: 44 pages
Submitted from: alexander.ullmann at gmx.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4217
or
http://arXiv.org/abs/1207.4217
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Diana Ojeda-Aristizabal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:06:46 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A norm for Tsirelson's Banach
space" by Diana Ojeda-Aristizabal.
Abstract: We give an expression for the norm of the space constructed by
Tsirelson. The implicit equation satisfied by this norm is dual to the
implicit equation for the norm of the dual of Tsirelson space given by
Figiel and Johnson. The expression can be modified to give the norm of
the dual of any mixed Tsirelson space. In particular, our results can
be adapted to give the norm for the dual of Schlumprecht space.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Submitted from: dco34 at cornell.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4504
or
http://arXiv.org/abs/1207.4504
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Manor Mendel and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:08:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Nonlinear spectral calculus and
super-expanders" by Manor Mendel and Assaf Naor.
Abstract: Nonlinear spectral gaps with respect to uniformly convex
normed spaces are shown to satisfy a spectral calculus inequality that
establishes their decay along Ces\`aro averages. Nonlinear spectral
gaps of graphs are also shown to behave sub-multiplicatively under
zigzag products. These results yield a combinatorial construction of
super-expanders, i.e., a sequence of 3-regular graphs that does not
admit a coarse embedding into any uniformly convex normed space.
Archive classification: math.MG math.CO math.FA
Remarks: Some of the results of this paper were announced in
arXiv:0910.2041.
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4705
or
http://arXiv.org/abs/1207.4705
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Waleed Noor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:09:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Embeddings of M\"{u}ntz spaces:
composition operators" by S. Waleed Noor.
Abstract: Given a strictly increasing sequence $\Lambda=(\lambda_n)$
of nonegative real numbers, with $\sum_{n=1}^\infty
\frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined
as the closure in $L^p([0,1])$ of the monomials $x^{\lambda_n}$. We
discuss how properties of the embedding $M_\Lambda^2\subset L^2(\mu)$,
where $\mu$ is a finite positive Borel measure on the interval $[0,1]$,
have immediate consequences for composition operators on $M^2_\Lambda$. We
give criteria for composition operators to be bounded, compact, or to
belong to the Schatten--von Neumann ideals.
Archive classification: math.FA
Mathematics Subject Classification: 46E15, 46E20, 46E35
Citation: Integral Equations Operator Theory, Springer, 2012
Remarks: 15 Pages
Submitted from: waleed_math at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.4719
or
http://arXiv.org/abs/1207.4719
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boris Rubin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:11:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Funk-Radon-Helgason
inversion method in integral geometry" by Boris Rubin.
Abstract: The paper deals with totally geodesic Radon transforms on
constant curvature spaces. We study applicability of the historically the
first Funk-Radon-Helgason method of mean value operators to reconstruction
of continuous and $L^p$ functions from their Radon transforms. New
inversion formulas involving Erd\'elyi-Kober type fractional integrals
are obtained. Particular emphasis is placed on the choice of the
differentiation operator in the spirit of the recent Helgason's formula.
Archive classification: math.FA
Mathematics Subject Classification: 44A12
Remarks: 29 pages
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.5178
or
http://arXiv.org/abs/1207.5178
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boris Rubin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:12:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Weighted norm inequalities for
k-plane transforms" by Boris Rubin.
Abstract: We obtain sharp inequalities for the k-plane transform, the
``j-plane to k-plane'' transform, and the corresponding dual transforms,
acting on $L^p$ spaces with a radial power weight. The operator
norms are
explicitly evaluated. Some generalizations and open problems are
discussed.
Archive classification: math.FA
Mathematics Subject Classification: 44A12
Remarks: 16 pages
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.5180
or
http://arXiv.org/abs/1207.5180
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas Hytonen and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:14:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Pisier's inequality revisited"
by Tuomas Hytonen and Assaf Naor.
Abstract: Given a Banach space $X$, for $n\in \mathbb N$ and $p\in
(1,\infty)$ we investigate the smallest constant $\mathfrak P\in
(0,\infty)$ for which every $f_1,\ldots,f_n:\{-1,1\}^n\to X$
satisfy \begin{multline*} \int_{\{-1,1\}^n}\Bigg\|\sum_{j=1}^n
\partial_jf_j(\varepsilon)\Bigg\|^pd\mu(\varepsilon)\\\le
\mathfrak{P}^p\int_{\{-1,1\}^n}\int_{\{-1,1\}^n}\Bigg\|\sum_{j=1}^n
\d_j\Delta f_j(\varepsilon)\Bigg\|^pd\mu(\varepsilon) d\mu(\delta),
\end{multline*} where $\mu$ is the uniform probability measure on
the discrete hypercube $\{-1,1\}^n$ and $\{\partial_j\}_{j=1}^n$ and
$\Delta=\sum_{j=1}^n\partial_j$ are the hypercube partial derivatives
and the hypercube Laplacian, respectively. Denoting this constant
by $\mathfrak{P}_p^n(X)$, we show that $\mathfrak{P}_p^n(X)\le
\sum_{k=1}^{n}\frac{1}{k}$ for every Banach space $(X,\|\cdot\|)$. This
extends the classical Pisier inequality, which corresponds to the special
case $f_j=\Delta^{-1}\partial_j f$ for some $f:\{-1,1\}^n\to X$. We show
that $\sup_{n\in \N}\mathfrak{P}_p^n(X)<\infty$ if either the dual $X^*$
is a $\mathrm{UMD}^+$ Banach space, or for some $\theta\in (0,1)$ we have
$X=[H,Y]_\theta$, where $H$ is a Hilbert space and $Y$ is an arbitrary
Banach space. It follows that $\sup_{n\in \N}\mathfrak{P}_p^n(X)<\infty$
if $X$ is a Banach lattice of finite cotype.
Archive classification: math.FA
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.5375
or
http://arXiv.org/abs/1207.5375
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Heinrich von Weizsacker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 26 Jul 2012 12:15:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "In which spaces every curve is
Lebesgue-Pettis-integrable?" by Heinrich von Weizsacker.
Abstract: In a real locally convex Hausdorff space the closed convex
hull of every metrizable compact set is compact if (and only if)
every continuous curve has a Pettis integral with respect to Lebesgue
measure. For such spaces there is a natural concept of Bochner integrals.
Archive classification: math.FA
Mathematics Subject Classification: 46G10
Submitted from: weizsaecker at mathematik.uni-kl.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.6034
or
http://arXiv.org/abs/1207.6034
Return-Path: <banach-bounces at math.okstate.edu>
Date: Mon, 13 Aug 2012 11:16:21 -0500
From: Dale Alspach <alspach at math.okstate.edu>
Subject: [Banach] nsc
Reply-To: tomek at math.huji.ac.il
Dear Colleagues,
The Institute of Mathematics of the Hebrew University is planning to
organize a memorial conference for Joram Lindenstrauss.
The conference, titled "Banach spaces: geometry and analysis"
will be held at the Institute of Advanced Studies of the Hebrew University
in Jerusalem , May 26-31, 2013.
More details will follow.
Organizers
Gideon Schechtman,
Tomek Szankowski,
Benjamin Weiss.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bjorn Kjos-Hanssen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 13:43:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Effective Banach spaces" by
Bjorn Kjos-Hanssen.
Abstract: This thesis addresses Pour-El and Richards' fourth question
from their book "Computability in analysis and physics", concerning
the relation between higher order recursion theory and computability
in analysis.
Among other things it is shown that there is a computability structure
that
is uncountable. The example given is a structure on the Banach space of
bounded linear operators on the set of almost periodic functions.
Archive classification: math.LO math.FA
Mathematics Subject Classification: 03D
Remarks: Master's thesis, University of Oslo, 1997. Adviser: Dag Normann.
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.6622
or
http://arXiv.org/abs/1207.6622
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jamilson Ramos Campos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 13:47:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Multiple Cohen strongly $p$-summing
operators, ideals, coherence and compatibility" by Jamilson Ramos
Campos.
Abstract: Considering the successful theory of multiple summing
multilinear operators as a prototype, we introduce the classes of multiple
Cohen strongly $p$-summing multilinear operators and polynomials. The
adequacy of these classes under the viewpoint of the theory of multilinear
and polynomial ideals is discussed in detail.
Archive classification: math.FA
Submitted from: jamilson at dce.ufpb.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.6664
or
http://arXiv.org/abs/1207.6664
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cleon S. Barroso, Michel P. Reboucas and
Marcus A. M. Marrocos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 13:51:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An interplay between the weak
form of Peano's theorem and structural aspects of Banach spaces"
by Cleon S. Barroso, Michel P. Reboucas and Marcus A. M. Marrocos.
Abstract: In this paper we establish some new results concerning the
Cauchy-Peano problem in Banach spaces. Firstly, we prove that if a Banach
space $E$ admits a fundamental biorthogonal system, then there exists
a continuous vector field $f\colon E\to E$ such that the autonomous
differential equation $u'=f(u)$ has no solutions at any time. The proof
relies on a key result asserting that every infinite-dimensional Fr\'echet
space with a fundamental biorthogonal system possesses a nontrivial
separable quotient. The later, is the byproduct of a mixture of known
results on barrelledness and two fundamental results of Banach space
theory (namely, a result of Pe{\l}czy\'nski on Banach spaces containing
$L_1(\mu)$ and the $\ell_1$-theorem of Rosenthal). Next, we introduce
a natural notion of weak-approximate solutions for the non-autonomous
Cauchy-Peano problem in Banach spaces, and prove that a necessary and
sufficient condition for the existence of such an approximation is the
absence of $\ell_1$-isomorphs inside the underline space. We also study a
kind of algebraic genericity for the Cauchy-Peano problem in spaces $E$
having complemented subspaces with unconditional Schauder basis. It is
proved that if $\mathscr{K}(E)$ denotes the family of all continuous
vector fields $f\colon E\to E$ for which $u'=f(u)$ has no solutions
at any time, then $\mathscr{K}(E)\bigcup \{0\}$ is spaceable in sense
that it contains a closed infinite dimensional subspace of $C(E)$,
the locally convex space of all continuous vector fields on $E$ with
the linear topology of uniform convergence on bounded sets.
Archive classification: math.FA
Remarks: 13 pages
Submitted from: cleonbar at mat.ufc.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.6777
or
http://arXiv.org/abs/1207.6777
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rolf Schneider and Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 13:54:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rotation invariant Minkowski
classes of convex bodies" by Rolf Schneider and Franz E. Schuster.
Abstract: A Minkowski class is a closed subset of the space of convex
bodies in Euclidean space Rn which is closed under Minkowski addition
and non-negative dilatations. A convex body in Rn is universal if the
expansion of its support function in spherical harmonics contains non-zero
harmonics of all orders. If K is universal, then a dense class of convex
bodies M has the following property. There exist convex bodies T1;
T2 such that M + T1 = T2, and T1; T2 belong to the rotation invariant
Minkowski class generated by K. It is shown that every convex body K
which is not centrally symmetric has a linear image, arbitrarily close
to K, which is universal. A modified version of the result holds for
centrally symmetric convex bodies. In this way, a result of S. Alesker
is strengthened, and at the same time given a more elementary proof.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 33C55
Citation: Mathematika 54 (2007), 1–13
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7286
or
http://arXiv.org/abs/1207.7286
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 13:57:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Volume inequalities and additive
maps of convex bodies" by Franz E. Schuster.
Abstract: Analogues of the classical inequalities from the
Brunn-Minkowski theory for rotation intertwining additive maps of
convex bodies are developed. Analogues are also proved of inequalities
from the dual Brunn-Minkowski theory for intertwining additive maps of
star bodies. These inequalities provide generalizations of results for
projection and intersection bodies. As a corollary, a new Brunn-Minkowski
inequality is obtained for the volume of polar projection bodies.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A40, 52A39
Citation: Mathematika 53 (2006), 211–234
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7290
or
http://arXiv.org/abs/1207.7290
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Peter M. Gruber and Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:05:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An arithmetic proof of John’s
ellipsoid theorem" by Peter M. Gruber and Franz E. Schuster.
Abstract: Using an idea of Voronoi in the geometric theory of positive
definite quadratic forms, we give a transparent proof of John’s
characterization of the unique ellipsoid of maximum volume contained
in a convex body. The same idea applies to the ‘hard part’ of a
generalization of John’s theorem and shows the difficulties of the
corresponding ‘easy part’.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A21, 46B07, 52A27
Citation: Arch. Math. (Basel) 85 (2005), 82–88
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7246
or
http://arXiv.org/abs/1207.7246
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:08:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Convolutions and multiplier
transformations of convex bodies" by Franz E. Schuster.
Abstract: Rotation intertwining maps from the set of convex bodies
in Rn into itself that are continuous linear operators with respect
to Minkowski and Blaschke addition are investigated. The main focus
is on Blaschke-Minkowski homomorphisms. We show that such maps are
represented by a spherical convolution operator. An application of this
representation is a complete classification of all even Blaschke-Minkowski
homomorphisms which shows that these maps behave in many respects similar
to the well known projection body operator. Among further applications
is the following result: If an even Blaschke-Minkowski homomorphism
maps a convex body to a polytope, then it is a constant multiple of the
projection body operator.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 43A90, 52A40
Citation: Trans. Amer. Math. Soc. 359 (2007), 5567–5591
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7252
or
http://arXiv.org/abs/1207.7252
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:12:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Crofton measures and Minkowski
valuations" by Franz E. Schuster.
Abstract: A description of continuous rigid motion compatible Minkowski
valuations is established. As an application, we present a Brunn-Minkowski
type inequality for intrinsic volumes of these valuations.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52B45, 43A90, 52A40
Citation: Duke Math. J. 154 (2010), 1–30
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7254
or
http://arXiv.org/abs/1207.7254
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Franz E. Schuster and Thomas Wannerer
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:15:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "GL(n) contravariant Minkowski
valuations" by Franz E. Schuster and Thomas Wannerer.
Abstract: A complete classification of all continuous GL(n) contravariant
Minkowski valuations is established. As an application we present a
family of sharp isoperimetric inequalities for such valuations which
generalize the classical Petty projection inequality.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52B45, 52A20, 52A40
Citation: Trans. Amer. Math. Soc. 364 (2012), 815–826
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7256
or
http://arXiv.org/abs/1207.7256
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gabriel Maresch and Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:18:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Sine transform of isotropic
measures" by Gabriel Maresch and Franz E. Schuster.
Abstract: Sharp isoperimetric inequalities for the sine transform of even
isotropic measures are established. The corresponding reverse inequalities
are obtained in an asymptotically optimal form. These new inequalities
have direct applications to strong volume estimates for convex bodies
from data about their sections or projections.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 52A41, 53Cxx
Citation: Int. Math. Res. Not. IMRN 2012, 717–739
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7266
or
http://arXiv.org/abs/1207.7266
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Lukas Parapatits and Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:21:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Steiner formula for Minkowski
faluations" by Lukas Parapatits and Franz E. Schuster.
Abstract: A Steiner type formula for continuous translation invariant
Minkowski valuations is established. In combination with a recent result
on the symmetry of rigid motion invariant homogeneous bivaluations, this
new Steiner type formula is used to obtain a family of Brunn-Minkowski
type inequalities for rigid motion intertwining Minkowski valuations.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52B45, 52A40
Citation: Adv. in Math. 230 (2012), 978-994
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7276
or
http://arXiv.org/abs/1207.7276
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rolf Schneider and Franz E. Schuster
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:24:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rotation equivariant Minkowski
valuations" by Rolf Schneider and Franz E. Schuster.
Abstract: The projection body operator \Pi, which associates with every
convex body in Euclidean space Rn its projection body, is a continuous
valuation, it is invariant under translations and equivariant under
rotations. It is also well known that \Pi\ maps the set of polytopes in
Rn into itself. We show that \Pi\ is the only non-trivial operator with
these properties.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 52B11, 52B45
Citation: Int. Math. Res. Not. 2006, Art. ID 72894, 20 pp
Submitted from: franz.schuster at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1207.7279
or
http://arXiv.org/abs/1207.7279
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jop Briet, Assaf Naor, and Oded Regev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:27:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Locally decodable codes and the
failure of cotype for projective tensor products" by Jop Briet, Assaf
Naor, and Oded Regev.
Abstract: It is shown that for every $p\in (1,\infty)$
there exists a Banach space $X$ of finite cotype such that
the projective tensor product $\ell_p\tp X$ fails to have
finite cotype. More generally, if $p_1,p_2,p_3\in (1,\infty)$
satisfy $\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}\le 1$ then
$\ell_{p_1}\tp\ell_{p_2}\tp\ell_{p_3}$ does not have finite cotype. This
is a proved via a connection to the theory of locally decodable codes.
Archive classification: math.FA cs.CC
Submitted from: odedr at cs.tau.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.0539
or
http://arXiv.org/abs/1208.0539
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alina Stancu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 25 Aug 2012 14:31:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some affine invariants revisited"
by Alina Stancu.
Abstract: We present several sharp inequalities for the $SL(n)$ invariant
$\Omega_{2,n}(K)$ introduced in our earlier work on centro-affine
invariants for smooth convex bodies containing the origin. A connection
arose with the Paouris-Werner invariant $\Omega_K$ defined for convex
bodies $K$ whose centroid is at the origin. We offer two alternative
definitions for $\Omega_K$ when $K \in C^2_+$. The technique employed
prompts us to conjecture that any $SL(n)$ invariant of convex bodies with
continuous and positive centro-affine curvature function can be obtained
as a limit of normalized $p$-affine surface areas of the convex body.
Archive classification: math.FA
Mathematics Subject Classification: 52A40, 52A38
Remarks: 15 pages
Submitted from: stancu at mathstat.concordia.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.0783
or
http://arXiv.org/abs/1208.0783
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ivan Feshchenko
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:27:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the divergence of series of
the form sum_{k=1}^infty||A_k x||^p" by Ivan Feshchenko.
Abstract: Let {A} be a system of operators. With any element x we
associate the set of elements {Ax}. We study conditions under which
there exists an element x such that the sum of p-th powers of norms of
the elements {Ax} is equal to infinity.
Archive classification: math.FA
Mathematics Subject Classification: 40H05, 46B20, 47A05
Remarks: 9 pages, submitted to Studia Mathematica
Submitted from: ivanmath007 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.1863
or
http://arXiv.org/abs/1208.1863
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. B. Abubaker, Fernanda Botelho and James
Jamison
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:31:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Representation of generalized
bi-circular projections on Banach spaces" by A. B. Abubaker, Fernanda
Botelho and James Jamison.
Abstract: We prove several results concerning the representation of
projections on arbitrary Banach spaces. We also give illustrative examples
including an example of a generalized bi-circular projection which can not
be written as the average of the identity with an isometric reflection. We
also characterize generalized bi-circular projections on $C_0(\Om,X)$,
with $\Om$ a locally compact Hausdorff space (not necessarily connected)
and $X$ a Banach space with trivial centralizer.
Archive classification: math.FA
Mathematics Subject Classification: 47B38, 47B15, 46B99, 47A65
Submitted from: abdullah at iitk.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.2012
or
http://arXiv.org/abs/1208.2012
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Grzegorz Plebanek, Jose
Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:34:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Baire measurability in
spaces of continuous functions" by Antonio Aviles, Grzegorz Plebanek,
Jose Rodriguez.
Abstract: Let C(K) be the Banach space of all continuous functions on a
given compact space K. We investigate the w*-sequential closure in C(K)*
of the set of all finitely supported probabilities on K. We discuss the
coincidence of the Baire sigma-algebras on C(K) associated to the weak
and pointwise convergence topologies.
Archive classification: math.FA
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.2207
or
http://arXiv.org/abs/1208.2207
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by E.Ostrovsky and L.Sirota
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:37:46 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Tchebyshev's characteristic of
rearrangement invariant space" by E.Ostrovsky and L.Sirota.
Abstract: We introduce and investigate in this short article a new
characteristic of rearrangement invariant (r.i.) (symmetric) space,
namely so-called Tchebychev's characteristic.
We reveal an important class of the r.i. spaces - so called regular
r. i. spaces and show that the majority of known r.i. spaces:
Lebesgue-Riesz, Grand Lebesgue Spaces, Orlicz, Lorentz and Marcinkiewicz
r.i. spaces are regular. But we construct after several examples of
r.i. spaces without the regular property.
Archive classification: math.FA
Submitted from: leos at post.sce.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.2393
or
http://arXiv.org/abs/1208.2393
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:40:02 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Determinacy of adversarial Gowers
games" by Christian Rosendal.
Abstract: We prove a game theoretic dichotomy for $G_{\delta\sigma}$
sets of block sequences in vector spaces that extends, on the one hand,
the block Ramsey theorem of W. T. Gowers proved for analytic sets of block
sequences and, on the other hand, M. Davis’ proof of $G_{\delta\sigma}$
determinacy.
Archive classification: math.LO math.FA
Submitted from: rosendal.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.2384
or
http://arXiv.org/abs/1208.2384
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by T.Banakh, A.Bartoszewicz, Sz.Glab, and
E.Szymonik
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:42:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Algebraic and topological
properties of some sets in $l_1$" by T.Banakh, A.Bartoszewicz, Sz.Glab,
and E.Szymonik.
Abstract: For a sequence $x \in l_1 \setminus c_{00}$, one can
consider the set $E(x)$ of all subsums of series $\sum_{n=1}^{\infty}
x(n)$. Guthrie and Nymann proved that $E(x)$ is one of the following
types of sets:
(I) a finite union of closed intervals; (C) homeomorphic to the Cantor
set; (MC) homeomorphic to the set $T$ of subsums of $\sum_{n=1}^\infty
b(n)$ where $b(2n-1) = 3/4^n$ and $b(2n) = 2/4^n$.
By $I$, $C$ and $MC$ we denote the sets of all sequences $x \in l_1
\setminus
c_{00}$, such that $E(x)$ has the corresponding property. In this note
we show that $I$ and $C$ are strongly $\mathfrak{c}$-algebrable and $MC$
is $\mathfrak{c}$-lineable. We show that $C$ is a dense $G_\delta$-set
in $l_1$ and $I$ is a true $F_\sigma$-set. Finally we show that $I$
is spaceable while $C$ is not spaceable.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 40A05, 15A03
Remarks: 15 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.3058
or
http://arXiv.org/abs/1208.3058
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miguel Lacruz and Maria del Pilar Romero de
la Rosa
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:46:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A local spectral condition for
strong compactness with some applications to bilateral weighted shifts"
by Miguel Lacruz and Maria del Pilar Romero de la Rosa.
Abstract: An algebra of bounded linear operators on a Banach space is
said to be {\em strongly compact} if its unit ball is precompact in
the strong operator topology, and a bounded linear operator on a Banach
space is said to be {\em strongly compact} if the algebra with identity
generated by the operator is strongly compact. Our interest in this
notion stems from the work of Lomonosov on the existence of invariant
subspaces. We provide a local spectral condition that is sufficient for
a bounded linear operator on a Banach space to be strongly compact. This
condition is then applied to describe a large class of strongly compact,
injective bilateral weighted shifts on Hilbert spaces, extending earlier
work of Fern\'andez-Valles and the first author. Further applications
are also derived, for instance, a strongly compact, invertible bilateral
weighted shift is constructed in such a way that its inverse fails to
be a strongly compact operator.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47B07
Remarks: 7 pages, to appear in Proc. Amer. Math. Soc
Submitted from: lacruz at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.3245
or
http://arXiv.org/abs/1208.3245
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miguel Lacruz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:50:03 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Hardy-Littlewood inequalities
for norms of positive operators on sequence spaces" by Miguel Lacruz.
Abstract: We consider estimates of Hardy and Littlewood for norms of
operators on sequence spaces, and we apply a factorization result of
Maurey to obtain improved estimates and simplified proofs for the special
case of a positive operator.
Archive classification: math.FA
Mathematics Subject Classification: 47B37
Remarks: 3 pages, to appear in Lin. Alg. Appl
Submitted from: lacruz at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.3246
or
http://arXiv.org/abs/1208.3246
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Erik Talvila
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 4 Sep 2012 14:56:00 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The $L^p$ primitive integral"
by Erik Talvila.
Abstract: For each $1\leq p<\infty$ a space of integrable Schwartz
distributions, $L{\!}'^{\,p}$, is defined by taking the distributional
derivative of all functions in $L^p$. Here, $L^p$ is with respect to
Lebesgue measure on the real line. If $f\in L{\!}'^{\,p}$ such that $f$ is
the distributional derivative of $F\in L^p$ then the integral is defined
as $\int^\infty_{-\infty} fG=-\int^\infty_{-\infty} F(x)g(x)\,dx$,
where $g\in L^q$, $G(x)= \int_0^x g(t)\,dt$ and $1/p+1/q=1$. A norm
is $\lVert f\rVert'_p=\lVert F\rVert_p$. The spaces $L{\!}'^{\,p}$
and $L^p$ are isometrically isomorphic. Distributions in $L{\!}'^{\,p}$
share many properties with functions in $L^p$. Hence, $L{\!}'^{\,p}$ is
reflexive, its dual space is identified with $L^q$, there is a type of
H\"older inequality, continuity in norm, convergence theorems, Gateaux
derivative. It is a Banach lattice and abstract $L$-space. Convolutions
and Fourier transforms are defined. Convolution with the Poisson kernel is
well-defined and provides a solution to the half plane Dirichlet problem,
boundary values being taken on in the new norm. A product is defined that
makes $L{\!}'^{\,1}$ into a Banach algebra isometrically isomorphic to
the convolution algebra on $L^1$. Spaces of higher order derivatives of
$L^p$ functions are defined. These are also Banach spaces isometrically
isomorphic to $L^p$.
Archive classification: math.CA math.FA
Mathematics Subject Classification: 46E30, 46F10, 46G12 (Primary) 42A38,
42A85, 46B42, 46C05 (Secondary)
Submitted from: Erik.Talvila at ufv.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.3694
or
http://arXiv.org/abs/1208.3694
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Peter G. Casazza
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:25:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The simplified version of the
Spielman and Sristave algorithm for proving the Bourgain-Tzafriri
restricted invertiblity theorem" by Peter G. Casazza.
Abstract: By giving up the best constants, we will see that the original
argument of Spielman and Sristave for proving the Bourgain-Tzafriri
Restricted Invertibility Theorem \cite{SS} still works - and is much
simplier than the final version. We do not intend on publishing this
since it is their argument with just a trivial modification, but we want
to make it available to the mathematics community since several people
have requested it already.
Archive classification: math.FA
Submitted from: casazzap at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.4013
or
http://arXiv.org/abs/1208.4013
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Svante Janson and Sten Kaijser
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:29:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Higher moments of Banach space
valued random variables" by Svante Janson and Sten Kaijser.
Abstract: We define the $k$:th moment of a Banach space valued random
variable as the expectation of its $k$:th tensor power; thus the moment
(if it exists) is an element of a tensor power of the original Banach
space. We study both the projective and injective tensor products,
and their relation. Moreover, in order to be general and flexible,
we study three different types of expectations: Bochner integrals,
Pettis integrals and Dunford integrals.
One of the problems studied is whether two random variables with
the same injective moments (of a given order) necessarily have the same
projective moments; this is of interest in applications. We show that
this holds if the Banach space has the approximation property, but not
in general. Several sections are devoted to results in special Banach
spaces, including Hilbert spaces, $C(K)$ and $D[0,1]$. The latter space
is non-separable, which complicates the arguments, and we prove various
preliminary results on e.g. measurability in $D[0,1]$ that we need.
One of the main motivations of this paper is the application to Zolotarev
metrics and their use in the contraction method. This is sketched in
an appendix.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60B11, 46G10
Remarks: 110 pages
Submitted from: svante.janson at math.uu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.4272
or
http://arXiv.org/abs/1208.4272
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kochanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:30:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stability of vector measures and
twisted sums of Banach spaces" by Tomasz Kochanek.
Abstract: A Banach space $X$ is said to have the $\mathsf{SVM}$ (stability
of vector measures) property if there exists a~constant $v<\infty$
such that for any algebra of sets $\mathcal F$, and any function
$\nu\colon\mathcal F\to X$ satisfying $$\|\nu(A\cup B)-\nu(A)-\nu(B)\|\leq
1\quad\mbox{for disjoint }A,B\in\mathcal F,$$there is a~vector measure
$\mu\colon\mathcal F\to X$ with $\|\nu(A)-\mu(A)\|\leq v$ for all
$A\in\mathcal F$. If this condition is valid when restricted to set
algebras $\mathcal F$ of cardinality less than some fixed cardinal
number $\kappa$, then we say that $X$ has the $\kappa$-$\mathsf{SVM}$
property. The least cardinal $\kappa$ for which $X$ does not have
the $\kappa$-$\mathsf{SVM}$ property (if it exists) is called the
$\mathsf{SVM}$ character of $X$. We apply the machinery of twisted sums
and quasi-linear maps to characterise these properties and to determine
$\mathsf{SVM}$ characters for many classical Banach spaces. We also
discuss connections between the $\kappa$-$\mathsf{SVM}$ property,
$\kappa$-injectivity and the `three-space' problem.
Archive classification: math.FA
Mathematics Subject Classification: Primary 28B05, 46G10, 46B25,
Secondary 46B03
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.4755
or
http://arXiv.org/abs/1208.4755
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by H. G. Dales, Tomasz Kania, Tomasz Kochanek, Piotr Koszmider, and Niels Jakob Laustsen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:32:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Maximal left ideals of the Banach
algebra of bounded operators on a Banach space" by H. G. Dales, Tomasz
Kania, Tomasz Kochanek, Piotr Koszmider, and Niels Jakob Laustsen.
Abstract: We address the following two questions regarding the maximal
left ideals of the Banach algebra $\mathscr{B}(E)$ of bounded operators
acting on an infinite-dimensional Banach space $E$:
(I) Does $\mathscr{B}(E)$ always contain a maximal left ideal which
is not finitely generated?
(II) Is every finitely-generated, maximal left ideal of $\mathscr{B}(E)$
necessarily of the form $\{ T\in\mathscr{B}(E) : Tx = 0\}$ (*) for some
non-zero $x\in E$?
Since the two-sided ideal $\mathscr{F}(E)$ of finite-rank operators
is not contained in any of the maximal left ideals given by (*), a
positive answer to the second question would imply a positive answer to
the first.
Our main results are: (i) Question (I) has a positive answer for most
(possibly all) infinite-dimensional Banach spaces; (ii) Question (II)
has a positive answer if and only if no finitely-generated, maximal left
ideal of $\mathscr{B}(E)$ contains $\mathscr{F}(E)$; (iii) the answer
to Question (II) is positive for many, but not all, Banach spaces.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary 47L10, 46H10, Secondary 47L20
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.4762
or
http://arXiv.org/abs/1208.4762
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Claudia Correa and Daniel V. Tausk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:34:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on the continuous self-maps
of the ladder system space" by Claudia Correa and Daniel V. Tausk.
Abstract: We give a partial characterization of the continuous self-maps
of the ladder system space K_S. Our results show that K_S is highly
nonrigid. We also discuss reasonable notions of "few operators" for
spaces C(K) with scattered K and we show that C(K_S) does not have few
operators for such notions.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 54G12, 46E15
Remarks: 5 pages
Submitted from: tausk at ime.usp.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.5454
or
http://arXiv.org/abs/1208.5454
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexey I. Popov and Adi Tcaciuc
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:35:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Every operator has almost-invariant
subspaces" by Alexey I. Popov and Adi Tcaciuc.
Abstract: We show that any bounded operator $T$ on a separable, reflexive,
infinite-dimensional Banach space $X$ admits a rank one perturbation which
has an invariant subspace of infinite dimension and codimension. In the
non-reflexive spaces, we show that the same is true for operators which
have non-eigenvalues in the boundary of their spectrum. In the Hilbert
space, our methods produce perturbations that are also small in norm,
improving on an old result of Brown and Pearcy.
Archive classification: math.FA
Mathematics Subject Classification: 47A15 (Primary) 47A55 (Secondary)
Remarks: 11 pages
Submitted from: atcaciuc at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.5831
or
http://arXiv.org/abs/1208.5831
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus Ferrer, Piotr Koszmider, and Wieslaw Kubis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:38:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Almost disjoint families of
countable sets and separable properties" by Jesus Ferrer, Piotr Koszmider,
and Wieslaw Kubis.
Abstract: We study the separable complementation property (SCP) and
its natural variations in Banach spaces of continuous functions over
compacta $K_{\mathcal A}$ induced by almost disjoint families ${\mathcal
A}$ of countable subsets of uncountable sets. For these spaces, we prove
among others that $C(K_{\mathcal A})$ has the controlled variant of the
separable complementation property if and only if $C(K_{\mathcal A})$
is Lindel\"of in the weak topology if and only if $K_{\mathcal A}$ is
monolithic. We give an example of ${\mathcal A}$ for which $C(K_{\mathcal
A})$ has the SCP, while $K_{\mathcal A}$ is not monolithic and an example
of a space $C(K_{\mathcal A})$ with controlled and continuous SCP which
has neither a projectional skeleton nor a projectional resolution of the
identity. Finally, we describe the structure of almost disjoint families
of cardinality $\omega_1$ which induce monolithic spaces of the form $K_{
\mathcal A}$: They can be obtained from countably many ladder systems
and pairwise disjoint families applying simple operations.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46E15, 03E75. Secondary:
46B20, 46B26
Remarks: 21 pages
Submitted from: kubis at math.cas.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.0199
or
http://arXiv.org/abs/1209.0199
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Koszmider and Saharon Shelah
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:40:02 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Independent families in Boolean
algebras with some separation" by Piotr Koszmider and Saharon Shelah.
Abstract: We prove that any Boolean algebra with the subsequential
completeness property contains an independent family of size
continuum. This improves a result of Argyros from the 80ties which
asserted the existence of an uncountable independent family. In fact we
prove it for a bigger class of Boolean algebras satisfying much weaker
properties. It follows that the Stone spaces of all such Boolean algebras
contains a copy of the Cech-Stone compactification of the integers and
the Banach space of contnuous functions on them has $l_\infty$ as a
quotient. Connections with the Grothendieck property in Banach spaces
are discussed.
Archive classification: math.LO math.FA math.GN
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.0177
or
http://arXiv.org/abs/1209.0177
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jian Ding, James R. Lee, and Yuval Peres
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:42:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Markov type and threshold
embeddings" by Jian Ding, James R. Lee, and Yuval Peres.
Abstract: For two metric spaces $X$ and $Y$, say that $X$ {\em
threshold-embeds into $Y$} if there exist a number $K > 0$ and a
family of Lipschitz maps $\{\varphi_{\tau} : X \to Y : \tau > 0
\}$ such that for every $x,y \in X$, $$ d_X(x,y) \geq \tau \implies
d_Y(\varphi_{\tau}(x),\varphi_{\tau}(y)) \geq \|\varphi_{\tau}\|_{\Lip}
\tau/K\,, $$ where $\|\varphi_{\tau}\|_{\Lip}$ denotes the Lipschitz
constant of $\varphi_{\tau}$. We show that if a metric space $X$
threshold-embeds into a Hilbert space, then $X$ has Markov type 2. As
a consequence, planar graph metrics and doubling metrics have Markov
type 2, answering questions of Naor, Peres, Schramm, and Sheffield. More
generally, if a metric space $X$ threshold-embeds into a $p$-uniformly
smooth Banach space, then $X$ has Markov type $p$.
The preceding result, together with Kwapien's theorem, is used to show
that if a Banach space threshold-embeds into a Hilbert space then it is
linearly isomorphic to a Hilbert space. This suggests some non-linear
analogs of Kwapien's theorem. For instance, a subset $X \subseteq L_1$
threshold-embeds into Hilbert space if and only if $X$ has Markov type 2.
Archive classification: math.MG math.FA math.PR
Submitted from: jrl at cs.washington.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.6088
or
http://arXiv.org/abs/1208.6088
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Nunez-Alarcon
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:46:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on the polynomial
Bohnenblust-Hille inequality" by Daniel Nunez-Alarcon.
Abstract: Recently, in paper published in the Annals of Mathematics,
it was shown that the Bohnenblust-Hille inequality for (complex)
homogeneous polynomials is hypercontractive. However, and to the best
of our knowledge, there is no result providing (nontrivial) lower bounds
for the optimal constants for n-homogeneous polynomials (n > 2). In this
short note we provide lower bounds for these famous constants.
Archive classification: math.FA
Submitted from: danielnunezal at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.6238
or
http://arXiv.org/abs/1208.6238
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anatolij Plichko
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 11 Sep 2012 09:47:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On uniform continuity of convex
bodies with respect to measures in Banach spaces" by Anatolij Plichko.
Abstract: Let $\mu$ be a probability measure on a separable Banach space
$X$. A subset $U\subset X$ is $\mu$-continuous if $\mu(\partial U)=0$. In
the paper the $\mu$-continuity and uniform $\mu$-continuity of convex
bodies in $X$, especially of balls and half-spaces, is considered. The
$\mu$-continuity is interesting for study of the Glivenko-Cantelli
theorem in Banach spaces. Answer to a question of F.~Tops{\o}e is given.
Archive classification: math.FA
Submitted from: aplichko at pk.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1208.6407
or
http://arXiv.org/abs/1208.6407
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. J. Dilworth, Denka Kutzarova, G.
Lancien, and N. L. Randrianarivony
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:18:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Asymptotic geometry of Banach
spaces and uniform quotient maps" by S. J. Dilworth, Denka Kutzarova,
G. Lancien, and N. L. Randrianarivony.
Abstract: Recently, Lima and Randrianarivony pointed out the role of
the property $(\beta)$ of Rolewicz in nonlinear quotient problems,
and answered a ten-year-old question of Bates, Johnson, Lindenstrauss,
Preiss and Schechtman. In the present paper, we prove that the modulus
of asymptotic uniform smoothness of the range space of a uniform quotient
map can be compared with the modulus of $(\beta)$ of the domain space. We
also provide conditions under which this comparison can be improved.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B80 (Primary), 46B20 (Secondary)
Submitted from: nrandria at slu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.0501
or
http://arXiv.org/abs/1209.0501
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:21:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Martingale inequalities and
operator space structures on $L_p$" by Gilles Pisier.
Abstract: We describe a new operator space structure on $L_p$ when $p$
is an even integer and compare it with the one introduced in our previous
work using complex interpolation. For the new structure, the Khintchine
inequalities and Burkholder's martingale inequalities have a very natural
form:\ the span of the Rademacher functions is completely isomorphic to
the operator Hilbert space $OH$, and the square function of a martingale
difference sequence $d_n$ is $\Sigma \ d_n\otimes \bar d_n$. Various
inequalities from harmonic analysis are also considered in the same
operator valued framework. Moreover, the new operator space structure
also makes sense for non commutative $L_p$-spaces with analogous results.
Archive classification: math.OA math.FA math.PR
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.1071
or
http://arXiv.org/abs/1209.1071
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stanislav Shkarin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:22:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Norm attaining operators and
pseudospectrum" by Stanislav Shkarin.
Abstract: It is shown that if $1<p<\infty$ and $X$ is a subspace or a
quotient of an $\ell_p$-direct sum of finite dimensional Banach spaces,
then for any compact operator $T$ on $X$ such that $\|I+T\|>1$, the
operator $I+T$ attains its norm. A reflexive Banach space $X$ and a
bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$
and $I+T$ does not attain its norm.
Archive classification: math.FA
Mathematics Subject Classification: 47A30, 47A10
Citation: Integral Equations and Operator Theory 64 (2009), 115-136
Submitted from: s.shkarin at qub.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.1218
or
http://arXiv.org/abs/1209.1218
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stanislav Shkarin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:24:22 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the spectrum of frequently
hypercyclic operators" by Stanislav Shkarin.
Abstract: A bounded linear operator $T$ on a Banach space $X$ is called
frequently hypercyclic if there exists $x\in X$ such that the lower
density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty
open subset $U$ of $X$. Bayart and Grivaux have raised a question whether
there is a frequently hypercyclic operator on any separable infinite
dimensional Banach space. We prove that the spectrum of a frequently
hypercyclic operator has no isolated points. It follows that there are
no frequently hypercyclic operators on all complex and on some real
hereditarily indecomposable Banach spaces, which provides a negative
answer to the above question.
Archive classification: math.FA math.DS
Mathematics Subject Classification: 47A16, 37A25
Citation: Proc. AMS 137 (2009), 123-134
Submitted from: s.shkarin at qub.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.1221
or
http://arXiv.org/abs/1209.1221
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. J. Dilworth, S. Gogyan, and Denka
Kutzarova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:32:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the convergence of a weak
greedy algorithm for the multivariate Haar basis" by S. J. Dilworth,
S. Gogyan, and Denka Kutzarova.
Abstract: We define a family of weak thresholding greedy algorithms
for the multivariate Haar basis for $L_1[0,1]^d$ ($d \ge 1$). We prove
convergence and uniform boundedness of the weak greedy approximants for
all $f \in L_1[0,1]^d$.
Archive classification: math.FA math.CA
Mathematics Subject Classification: Primary: 41A65. Secondary: 42A10,
46B20
Remarks: 25 pages
Submitted from: dilworth at math.sc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.1378
or
http://arXiv.org/abs/1209.1378
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by P.A.H. Brooker and G. Lancien
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:36:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Three-space property for
asymptotically uniformly smooth renormings" by P.A.H. Brooker and
G. Lancien.
Abstract: We prove that if $Y$ is a closed subspace of a Banach space
$X$ such that $Y$ and $X/Y$ admit an equivalent asymptotically uniformly
smooth norm, then $X$ also admits an equivalent asymptotically uniformly
smooth norm. The proof is based on the use of the Szlenk index and yields
a few other applications to renorming theory.
Archive classification: math.FA
Submitted from: gilles.lancien at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.1567
or
http://arXiv.org/abs/1209.1567
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:39:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantum expanders and geometry
of operator spaces" by Gilles Pisier.
Abstract: We show that there are well separated families of quantum
expanders with asymptotically the maximal cardinality allowed by a known
upper bound. This has applications to the ``local theory" of operator
spaces. This allows us to provide sharp estimates for the growth of the
multiplicity of $M_N$-spaces needed to represent (up to a constant $C>1$)
the $M_N$-version of the $n$-dimensional operator Hilbert space $OH_n$
as a direct sum of copies of $M_N$. We show that, when $C$ is close
to 1, this multiplicity grows as $\exp{\beta n N^2}$ for some constant
$\beta>0$. The main idea is to identify quantum expanders with ``smooth"
points on the matricial analogue of the unit sphere. This generalizes to
operator spaces a classical geometric result on $n$-dimensional Hilbert
space (corresponding to $N=1$). Our work strongly suggests to further
study a certain class of operator spaces that we call matricially
subGaussian.
In a second part, we introduce and study a generalization of the
notion of exact operator space that we call subexponential. Using Random
Matrices we show that the factorization results of Grothendieck type that
are known in the exact case all extend to the subexponential case, and we
exhibit (a continuum of distinct) examples of non-exact subexponential
operator spaces. We also show that $OH$, $R+C$ and $\max(\ell_2)$
(or any other maximal operator space) are not subexponential.
Archive classification: math.OA math-ph math.FA math.MP
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.2059
or
http://arXiv.org/abs/1209.2059
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. V. Kislyakov, D. V. Maksimov, and D. M.
Stolyarov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 20 Sep 2012 10:41:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Differential expressions with
mixed homogeneity and spaces of smooth functions they generate"
by S. V. Kislyakov, D. V. Maksimov, and D. M. Stolyarov.
Abstract: Let $\{T_1,\dots,T_l\}$ be a collection of differential
operators with constant coefficients on the torus $\mathbb{T}^n$. Consider
the Banach space $X$ of functions $f$ on the torus for which all functions
$T_j f$, $j=1,\dots,l$, are continuous. Extending the previous work of
the first two authors, we analyse the embeddability of $X$ into some
space $C(K)$ as a complemented subspace. We prove the following. Fix some
pattern of mixed homogeneity and extract the senior homogeneous parts
(relative to the pattern chosen) $\{\tau_1,\dots,\tau_l\}$ from the
initial operators $\{T_1,\dots,T_l\}$. Let $N$ be the dimension of the
linear span of $\{\tau_1,\dots,\tau_l\}$. If $N\geqslant 2$, then $X$
is not isomorphic to a complemented subspace of $C(K)$ for any compact
space $K$.
The main ingredient of the proof of this fact is a new Sobolev-type
embedding theorem.
Archive classification: math.FA math.CA
Remarks: 37 pages
Submitted from: dms239 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.2078
or
http://arXiv.org/abs/1209.2078
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles and Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 13:59:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A Banach space in which every
injective operator is surjective" by Antonio Aviles and Piotr Koszmider.
Abstract: We construct an infinite dimensional Banach space of continuous
functions C(K) such that every one-to-one operator on C(K) is onto.
Archive classification: math.FA math.GN
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.3042
or
http://arXiv.org/abs/1209.3042
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miguel Martin and Yoshimichi Ueda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:01:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the geometry of von Neumann
algebra preduals" by Miguel Martin and Yoshimichi Ueda.
Abstract: Let $M$ be a von Neumann algebra and let $M_\star$ be its
(unique) predual. We study when for every $\varphi\in M_\star$
there exists $\psi\in M_\star$ solving the equation $\|\varphi \pm
\psi\|=\|\varphi\|=\|\psi\|$. This is the case when $M$ does not contain
type I nor type III$_1$ factors as direct summands and it is false at
least for the unique hyperfinite type III$_1$ factor. An approximate
result valid for all diffuse von Neumann algebras allows to show that the
equation has solution for every element in the ultraproduct of preduals
of diffuse von Neumann algebras and, in particular, the dual von Neumann
algebra of such ultraproduct is diffuse. This shows that the Daugavet
property and the uniform Daugavet property are equivalent for preduals
of von Neumann algebras.
Archive classification: math.OA
Remarks: 9 pages
Submitted from: ueda at math.kyushu-u.ac.jp
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.3391
or
http://arXiv.org/abs/1209.3391
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Raf Cluckers and Daniel J. Miller
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:03:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lebesgue classes and preparation
of real constructible functions" by Raf Cluckers and Daniel J. Miller.
Abstract: We call a function constructible if it has a globally
subanalytic domain and can be expressed as a sum of products of globally
subanalytic functions and logarithms of positively-valued globally
subanalytic functions. For any $q > 0$ and constructible functions
$f$ and $\mu$ on $E\times\RR^n$, we prove a theorem describing the
structure of the set of all $(x,p)$ in $E \times (0,\infty]$ for which
$y \mapsto f(x,y)$ is in $L^p(|\mu|_{x}^{q})$, where $|\mu|_{x}^{q}$
is the positive measure on $\RR^n$ whose Radon-Nikodym derivative with
respect to the Lebesgue measure is $y\mapsto |\mu(x,y)|^q$. We also prove
a closely related preparation theorem for $f$ and $\mu$. These results
relate analysis (the study of $L^p$-spaces) with geometry (the study of
zero loci).
Archive classification: math.AG math.FA math.LO
Mathematics Subject Classification: 46E30, 32B20, 14P15 (Primary) 42B35,
03C64 (Secondary)
Submitted from: dmille10 at emporia.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.3439
or
http://arXiv.org/abs/1209.3439
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eleonora Cinti and Aldo Pratelli
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:05:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The $\epsilon-\epsilon^\beta$
property, the boundedness of isoperimetric sets in $\R^N$ with density,
and some applications" by Eleonora Cinti and Aldo Pratelli.
Abstract: We show that every isoperimetric set in R^N with density is
bounded if the density is continuous and bounded by above and below. This
improves the previously known boundedness results, which basically
needed a Lipschitz assumption; on the other hand, the present assumption
is sharp, as we show with an explicit example. To obtain our result,
we observe that the main tool which is often used, namely a classical
``\epsilon-\epsilon'' property already discussed by Allard, Almgren
and Bombieri, admits a weaker counterpart which is still sufficient for
the boundedness, namely, an ``\epsilon-\epsilon^\beta'' version of the
property. And in turn, while for the validity of the first property the
Lipschitz assumption is essential, for the latter the sole continuity
is enough. We conclude by deriving some consequences of our result about
the existence and regularity of isoperimetric sets.
Archive classification: math.FA
Submitted from: eleonora.cinti at unipv.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.3624
or
http://arXiv.org/abs/1209.3624
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles and Stevo Todorcevic
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:09:24 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Analytic multiple gaps" by Antonio
Aviles and Stevo Todorcevic.
Abstract: We prove that there is a finite basis for analytic n-gaps,
and we prove a number of results concerning the structure of an analytic
n-gap when restricted to an infinite subset. This has applications in
the study of how different classes of subsequences are mixed inside a
sequence of vectors in a Banach space
Archive classification: math.LO math.CO math.FA
Mathematics Subject Classification: Primary 03E15, 28A05, 05D10,
Secondary 46B15
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.3751
or
http://arXiv.org/abs/1209.3751
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Paul F. X. Mueller
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:11:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A decomposition for Hardy
martingales. Part II" by Paul F. X. Mueller.
Abstract: We prove Davis and Garsia Inequalities for dyadic perturbations
of Hardy Martingales. We apply those to estimate the $L^1 $ distance
of a dyadic martingale to the class of Hardy martingales. We revisit
Bourgains embedding of $L^1$ into the quotient space $ L^1 / H^1 . $
Archive classification: math.FA math.CV
Submitted from: pfxm at bayou.uni-linz.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.3964
or
http://arXiv.org/abs/1209.3964
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez and Jesus Bastero
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:13:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The variance conjecture on some
polytopes" by David Alonso-Gutierrez and Jesus Bastero.
Abstract: We show that any random vector uniformly distributed on any
hyperplane projection of $B_1^n$ or $B_\infty^n$ verifies the variance
conjecture $$\text{Var }|X|^2\leq C\sup_{\xi\in S^{n-1}}\E\langle
X,\xi\rangle^2\E|X|^2.$$ Furthermore, a random vector uniformly
distributed on a hyperplane projection of $B_\infty^n$ verifies a negative
square correlation property and consequently any of its linear images
verifies the variance conjecture.
Archive classification: math.FA
Submitted from: bastero at unizar.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.4270
or
http://arXiv.org/abs/1209.4270
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:14:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Universal objects and associations
between classes of Banach spaces classes of compact spaces" by Piotr
Koszmider.
Abstract: In the context of classical associations between classes of
Banach spaces and classes of compact Hausdorff spaces we survey known
results and open questions concerning the existence and nonexistence
of universal Banach spaces and of universal compact spaces in various
classes. This gives quite a complex network of interrelations which
quite often depend on additional set-theoretic assumptions.
Archive classification: math.FA math.GN math.LO
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.4294
or
http://arXiv.org/abs/1209.4294
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Almut Burchard and Gregory R. Chambers
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:16:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Perimeter under multiple Steiner
symmetrizations" by Almut Burchard and Gregory R. Chambers.
Abstract: Steiner symmetrization along n linearly independent directions
transforms every compact subset of R^n into a set of finite perimeter.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 28A75 (26B15, 52A38)
Remarks: 12 pages, 1 figure
Submitted from: almut at math.toronto.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.4521
or
http://arXiv.org/abs/1209.4521
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D. Pellegrino and J.B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:18:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Bohnenblust-Hille inequality
for real homogeneous polynomials is hypercontractive and this result
is optimal" by D. Pellegrino and J.B. Seoane-Sepulveda.
Abstract: It was recently shown by A. Montanaro that the low growth of
the constants of the multilinear Bohnenblust-Hille inequality, for real
scalars, plays a crucial role in Quantum Information Theory. In this
paper, among other results, we show that the polynomial Bohnenblust--Hille
inequality, for real scalars, is hypercontractive; the case of complex
scalars was recently proved in the paper "The Bohnhenblust-Hille
inequality for homogeneous polynomials is hypercontractive" , by Defant,
Frerick, Ortega-Cerd\'{a}, Ouna\"{\i}es, and Seip (Annals of Mathematics,
2011). Our proof is presented in a simple form, by making use of a deep
result that dates back to Erd\"os (Bull. Amer. Math. Soc., 1947). We
also show, in strong contrast to what happens in the case of multilinear
mappings, that the hypercontractive growth of these constants cannot be
improved. The complex version of this result remains still open.
Archive classification: math.FA
Mathematics Subject Classification: 46G25, 30B50
Submitted from: jseoane at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.4632
or
http://arXiv.org/abs/1209.4632
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kochanek and Michal Lewicki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:20:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Characterisation of $L_p$-norms
via H\"older's inequality" by Tomasz Kochanek and Michal Lewicki.
Abstract: We characterise $L_p$-norms on the space of integrable
step functions, defined on a probabilistic space, via H\"older's type
inequality with an optimality condition.
Archive classification: math.FA
Mathematics Subject Classification: 26D15, 39B05, 46B04
Submitted from: t_kochanek at wp.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.4587
or
http://arXiv.org/abs/1209.4587
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D. Freeman, E. Odell, Th. Schlumprecht, and
A. Zsak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:21:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Unconditional structures of
translates for $L_p(R^d)$" by D. Freeman, E. Odell, Th. Schlumprecht,
and A. Zsak.
Abstract: We prove that a sequence $(f_i)_{i=1}^\infty$ of translates of a
fixed $f\in L_p(R)$ cannot be an unconditional basis of $L_p(R)$ for any
$1\le p<\infty$. In contrast to this, for every $2<p<\infty$, $d\in N$
and unbounded sequence $(\lambda_n)_{n\in N}\subset R^d$ we establish
the existence of a function $f\in L_p(R^d)$ and sequence $(g^*_n)_{n\in
N}\subset L_p^*(R^d)$ such that $(T_{\lambda_n} f, g^*_n)_{n\in N}$
forms an unconditional Schauder frame for $L_p(R^d)$. In particular,
there exists a Schauder frame of integer translates for $L_p(R)$ if
(and only if) $2<p<\infty$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 54H05, 42C15
Remarks: 22 pages
Submitted from: dfreema7 at slu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.4619
or
http://arXiv.org/abs/1209.4619
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by C. Ruiz, J. Lopez-Abad and P. Tradacete
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:23:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The convex hull of a Banach-Saks
set" by C. Ruiz, J. Lopez-Abad and P. Tradacete.
Abstract: A subset $A$ of a Banach space is called Banach-Saks when every
sequence in $A$ has a Ces{\`a}ro convergent subsequence. Our interest here
focusses on the following problem: is the convex hull of a Banach-Saks
set again Banach-Saks? By means of a combinatorial argument, we show
that in general the answer is negative. However, sufficient conditions
are given in order to obtain a positive result.
Archive classification: math.FA math.CO math.LO
Mathematics Subject Classification: 46B50, 05D10
Remarks: 29 pages
Submitted from: abad at icmat.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.4851
or
http://arXiv.org/abs/1209.4851
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander E. Litvak, Mark Rudelson, and
Nicole Tomczak-Jaegermann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 28 Sep 2012 14:24:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On approximations by projections
of polytopes with few facets" by Alexander E. Litvak, Mark Rudelson,
and Nicole Tomczak-Jaegermann.
Abstract: We provide an affirmative answer to a problem posed by
Barvinok and Veomett, showing that in general an n-dimensional convex
body cannot be approximated by a projection of a section of a simplex
of a sub-exponential dimension. Moreover, we establish a lower bound of
the Banach-Mazur distance between n-dimensional projections of sections
of an N-dimensional simplex and a certain convex symmetric body, which
is sharp up to a logarithmic factor for all N>n.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary: 52A23, 52A27, Secondary:
52B55, 46B09
Remarks: 22 pages
Submitted from: rudelson at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1209.6281
or
http://arXiv.org/abs/1209.6281
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Florent P. Baudier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:24:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantitative nonlinear embeddings
into Lebesgue sequence spaces" by Florent P. Baudier.
Abstract: In this paper coarse, uniform and strong embeddings of metric
spaces into Lebesgue sequence spaces are studied in their quantitative
aspects. In particular, strong deformation gaps are obtained when
embedding strongly a Hilbert space into $\ell_p$ for $0<p< 2$ as well as
new insights on the nonlinear geometry of the spaces $L_p$ and $\ell_p$
for $0<p<1$. The exact $\ell_q$-compression of $\ell_p$-spaces is
computed. Finally the coarse deformation of metric spaces with property
A and amenable groups is investigated.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B20, 46B85, 46T99, 20F65
Submitted from: florent at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.0588
or
http://arXiv.org/abs/1210.0588
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Costas Poulios
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:26:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Non-separable tree-like Banach
spaces and Rosenthal's $\ell_1$-theorem " by Costas Poulios.
Abstract: We introduce and investigate a class of non-separable tree-like
Banach spaces. As a consequence, we prove that we can not achieve a
satisfactory extension of Rosenthal's $\ell_1$-theorem to spaces of the
type $\ell_1(\kappa)$, for $\kappa$ an uncountable cardinal.
Archive classification: math.FA
Mathematics Subject Classification: 46B25, 46B26
Submitted from: k-poulios at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.0792
or
http://arXiv.org/abs/1210.0792
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan-David Hardtke
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:28:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On convergence with respect to
an ideal and a family of matrices" by Jan-David Hardtke.
Abstract: Recently P. Das, S. Dutta and E. Savas introduced and
studied the notions of strong $A^I$-summability with respect to an
Orlicz function $F$ and $A^I$-statistical convergence, where $A$ is a
non-negative regular matrix and $I$ is an ideal on the set of natural
numbers. In this note, we will generalise these notions by replacing $A$
with a family of matrices and $F$ with a family of Orlicz functions or
moduli and study the thus obtained convergence methods. We will also
give an application in Banach space theory, presenting a generalisation
of Simons' $\sup$-$\limsup$-theorem to the newly introduced convergence
methods (for the case that the filter generated by the ideal $I$ has a
countable base), continuing the author's previous work.
Archive classification: math.FA
Mathematics Subject Classification: 40C05, 40C99, 46B20
Remarks: 32 pages
Submitted from: hardtke at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.1350
or
http://arXiv.org/abs/1210.1350
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by E.Ostrovsky and L.Sirota
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:31:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A Banach rearrangement norm
characterization for tail behavior of measurable functions (random
variables)" by E.Ostrovsky and L.Sirota.
Abstract: We construct a Banach rearrangement invariant norm on the
measurable space for which the finiteness of this norm for measurable
function (random variable) is equivalent to suitable tail (heavy tail
and light tail) behavior.
We investigate also a conjugate to offered spaces and obtain some
embedding theorems. Possible applications: Functional Analysis (for
instance, interpolation of operators), Integral Equations, Probability
Theory and Statistics (tail estimations for random variables).
Archive classification: math.FA math.PR
Submitted from: leos at post.sce.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.1168
or
http://arXiv.org/abs/1210.1168
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Henning Kempka and Jan Vybiral
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:32:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lorentz spaces with variable
exponents" by Henning Kempka and Jan Vybiral.
Abstract: We introduce Lorentz spaces $L_{p(\cdot),q}(\R^n)$ and
$L_{p(\cdot),q(\cdot)}(\R^n)$ with variable exponents. We prove several
basic properties of these spaces including embeddings and the identity
$L_{p(\cdot),p(\cdot)}(\R^n)=L_{p(\cdot)}(\R^n)$. We also show that
these spaces arise through real interpolation between $L_{\p}(\R^n)$
and $L_\infty(\R^n)$. Furthermore, we answer in a negative way the
question posed in \cite{DHN} whether the Marcinkiewicz interpolation
theorem holds in the frame of Lebesgue spaces with variable integrability.
Archive classification: math.FA
Submitted from: henning.kempka at uni-jena.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.1738
or
http://arXiv.org/abs/1210.1738
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S.A. Argyros, A. Manoussakis, and M.
Petrakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:34:03 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Function spaces not containing
$\ell_{1}$" by S.A. Argyros, A. Manoussakis, and M. Petrakis.
Abstract: For $\Omega$ bounded and open subset of $\mathbb{R}^{d_{0}}$
and $X$ a reflexive Banach space with $1$-symmetric basis, the function
space $JF_{X}(\Omega)$ is defined. This class of spaces includes the
classical James function space. Every member of this class is separable
and has non-separable dual. We provide a proof of topological nature that
$JF_{X}(\Omega)$ does not contain an isomorphic copy of $\ell_{1}$. We
also investigate the structure of these spaces and their duals.
Archive classification: math.FA
Mathematics Subject Classification: 46B10
Citation: Israel Journal of Mathematics 135 (2003), 29-81
Submitted from: amanousakis at isc.tuc.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.2379
or
http://arXiv.org/abs/1210.2379
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Geraldo Botelho, Daniel Pellegrino, and
Pilar Rueda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:36:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Pietsch measures for summing
operators and dominated polynomials" by Geraldo Botelho, Daniel
Pellegrino, and Pilar Rueda.
Abstract: We relate the injectivity of the canonical map from $C(B_{E'})$
to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on
the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$
endowed with the weak* topology, to the existence of injective $p$-summing
linear operators/$p$-dominated homogeneous polynomials defined on $E$
having $\mu$ as a Pietsch measure. As an application we fill the gap in
the proofs of some results of concerning Pietsch-type factorization of
dominated polynomials.
Archive classification: math.FA
Mathematics Subject Classification: 28C15, 46G25, 47B10, 47L22
Remarks: 13 pages
Submitted from: pilar.rueda at uv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.3332
or
http://arXiv.org/abs/1210.3332
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Philip A.H. Brooker
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 16 Oct 2012 13:38:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Szlenk and $w^\ast$-dentability
indices of the Banach spaces $C([0,\alpha])$" by Philip A.H. Brooker.
Abstract: Let $\alpha$ be an infinite ordinal and $\gamma$ the
unique ordinal satisfying $\omega^{\omega^\gamma}\leq \alpha
< \omega^{\omega^{\gamma+1}}$. We show that the Banach space
$C([0,\,\alpha])$ of all continuous scalar-valued functions on the
compact ordinal interval $[0,\,\alpha]$ has Szlenk index equal
to $\omega^{\gamma+1}$ and $w^\ast$-dentability index equal to
$\omega^{1+\gamma+1}$.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B20
Submitted from: philip.a.h.brooker at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.3696
or
http://arXiv.org/abs/1210.3696
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stephan Fackler
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Oct 2012 12:38:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Kalton-Lancien theorem
revisited: Maximal regularity does not extrapolate" by Stephan Fackler.
Abstract: We give a new more explicit proof of a result by Kalton &
Lancien stating that on each Banach space with an unconditional basis not
isomorphic to a Hilbert space there exists a generator of a holomorphic
semigroup which does not have maximal regularity. In particular, we show
that there always exists a Schauder basis (f_m) such that the generator
is a Schauder multiplier associated to the sequence (2^m). Moreover,
we show that maximal regularity does not extrapolate: we construct
consistent holomorphic semigroups (T_p(t)) on L^p for p in (1, \infty)
which have maximal regularity if and only if p = 2. These assertions
were both open problems. Our approach is completely different than the
one of Kalton & Lancien. We use the characterization of maximal regularity
by R-sectoriality for our construction.
Archive classification: math.FA math.AP
Mathematics Subject Classification: 35K90, 47D06 (Primary) 46B15
(Secondary)
Remarks: 16 pages
Submitted from: stephan.fackler at uni-ulm.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.4333
or
http://arXiv.org/abs/1210.4333
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vitali Milman and Liran Rotem
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Oct 2012 12:40:18 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Mixed integrals and related
inequalities" by Vitali Milman and Liran Rotem.
Abstract: In this paper we define an addition operation on the class
of quasi-concave functions. While the new operation is similar to the
well-known sup-convolution, it has the property that it polarizes the
Lebesgue integral. This allows us to define mixed integrals, which are
the functional analogs of the classic mixed volumes.
We extend various classic inequalities, such as the Brunn-Minkowski and
the Alexandrov-Fenchel inequality, to the functional setting. For
general quasi-concave functions, this is done by restating those results
in the language of rearrangement inequalities. Restricting ourselves
to log-concave functions, we prove generalizations of the Alexandrov
inequalities in a more familiar form.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A39, 26B25
Remarks: 30 pages
Submitted from: liranro1 at post.tau.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.4346
or
http://arXiv.org/abs/1210.4346
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ludek Zajicek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Oct 2012 12:42:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Hadamard differentiability via
Gateaux differentiability" by Ludek Zajicek.
Abstract: Let $X$ be a separable Banach space, $Y$ a Banach space and $f:
X \to Y$ a mapping. We prove that there exists a $\sigma$-directionally
porous set $A\subset X$ such that if $x\in X \setminus A$, $f$ is
Lipschitz at $x$, and $f$ is G\^ateaux differentiable at $x$, then $f$
is Hadamard differentiable at $x$.
If $f$ is Borel measurable (or has the Baire property) and is G\^ ateaux
differentiable at all points, then $f$ is Hadamard differentiable at
all points except a set which is $\sigma$-directionally porous set
(and so is Aronszajn null, Haar null and $\Gamma$-null). Consequently,
an everywhere G\^ ateaux differentiable $f: \R^n \to Y$ is Fr\' echet
differentiable except a nowhere dense $\sigma$-porous set.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46G05, Secondary: 26B05,
49J50
Remarks: 9 pages
Submitted from: zajicek at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.4715
or
http://arXiv.org/abs/1210.4715
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rafa Espinola and Miguel Lacruz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Oct 2012 12:44:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Applications of fixed point
theorems in the theory of invariant subspaces" by Rafa Espinola and
Miguel Lacruz.
Abstract: We survey several applications of fixed point theorems in the
theory of invariant subspaces. The general idea is that a fixed point
theorem applied to a suitable map yields the existence of invariant
subspaces for an operator on a Banach space.
Archive classification: math.OA
Mathematics Subject Classification: 47A15, 47H10
Remarks: 13 pages, to appear in Fixed Point Theory and Applications
Submitted from: lacruz at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.5557
or
http://arXiv.org/abs/1210.5557
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by J. Lopez-Abad
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Oct 2012 12:45:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A Bourgain-Pisier construction
for general Banach spaces" by J. Lopez-Abad.
Abstract: We prove that every Banach space, not necessarily separable,
can be isometrically embedded into a $\mathcal L_{\infty}$-space in a
way that the corresponding quotient has the Radon-Nikodym and the Schur
properties. As a consequence, we obtain $\mathcal L_\infty$ spaces
of arbitrary large densities with the Schur and the Radon-Nikodym
properties. This extents the a classical result by J. Bourgain and
G. Pisier.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B26
Submitted from: abad at icmat.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.5728
or
http://arXiv.org/abs/1210.5728
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Enrique A. Sanchez Perez and Dirk Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 09:54:17 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Slice continuity for operators
and the Daugavet property for bilinear maps" by Enrique A. Sanchez Perez
and Dirk Werner.
Abstract: We introduce and analyse the notion of slice continuity between
operators on Banach spaces in the setting of the Daugavet property.
It is shown that under the slice continuity assumption the Daugavet
equation holds for weakly compact operators. As an application we
define and characterise the Daugavet property for bilinear maps, and
we prove that this allows us to describe some $p$-convexifications of
the Daugavet equation for operators on Banach function spaces that have
recently been introduced.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, secondary 46B25
Submitted from: werner at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.7099
or
http://arXiv.org/abs/1210.7099
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dongni Tan, Xujian Huang, and Rui Liu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 09:55:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Generalized-Lush Spaces and the
Mazur-Ulam Property" by Dongni Tan, Xujian Huang, and Rui Liu.
Abstract: We introduce a new class of Banach spaces, called
generalized-lush spaces (GL-spaces for short), which contains
almost-CL-spaces, separable lush spaces (specially, separable $C$-rich
subspaces of $C(K)$), and even the two-dimensional space with hexagonal
norm. We obtain that the space $C(K,E)$ of the vector-valued continuous
functions is a GL-space whenever $E$ is, and show that the GL-space
is stable under $c_0$-, $l_1$- and $l_\infty$-sums. As an application,
we prove that the Mazur-Ulam property holds for a larger class of Banach
spaces, called local-GL-spaces, including all lush spaces and GL-spaces.
Furthermore, we generalize the stability properties of GL-spaces to
local-GL-spaces. From this, we can obtain many examples of Banach spaces
having the Mazur-Ulam property.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, Secondary 46B20, 46A22
Remarks: 16 pages
Submitted from: ruiliu at nankai.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.7324
or
http://arXiv.org/abs/1210.7324
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Shanwen Hu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 09:57:25 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Least squares problems in
orthornormalization" by Shanwen Hu.
Abstract: For any $n$-tuple $(\alpha_1,\cdots,\alpha_n)$ of
linearly independent vectors in Hilbert space $H$, we construct
a unique orthonormal basis $(\epsilon_1,\cdots,\epsilon_n)$
of $span\{\alpha_1,\cdots,\alpha_n\}$ satisfying:
$$\sum_{i=1}^n\|\epsilon_i-\alpha_i\|^2\le\sum_{i=1}^n\|\beta_i-\alpha_i\|^2$$
for all orthonormal basis $(\beta_1,\cdots,\beta_n)$ of
$span\{\alpha_1,\cdots,\alpha_n\}$.
We study the stability of the orthornormalization and give some
applications and examples.
Archive classification: math.FA
Remarks: 10 pages
Submitted from: swhu at math.ecnu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1210.7400
or
http://arXiv.org/abs/1210.7400
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Constantinos Kardaras
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 09:58:38 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uniform integrability and local
convexity in $L^0$" by Constantinos Kardaras.
Abstract: Let $L^0$ be the vector space of all (equivalence classes of)
real-valued random variables built over a probability space $(\Omega,
\mathcal{F}, P)$, equipped with a metric topology compatible with
convergence in probability. In this work, we provide a necessary
and sufficient structural condition that a set $X \subseteq L^0$
should satisfy in order to infer the existence of a probability
$Q$ that is equivalent to $P$ and such that $X$ is uniformly
$Q$-integrable. Furthermore, we connect the previous essentially
measure-free version of uniform integrability with local convexity of
the $L^0$-topology when restricted on convex, solid and bounded subsets
of $L^0$.
Archive classification: math.FA math.PR
Remarks: 14 pages
Submitted from: langostas at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.0475
or
http://arXiv.org/abs/1211.0475
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:30:53 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantum expanders and geometry
of operator spaces II" by Gilles Pisier.
Abstract: In this appendix to our paper with the same title posted on
arxiv we give a quick proof of an inequality that can be substituted
to Hastings's result, quoted as Lemma 1.9 in our previous paper. Our
inequality is less sharp but also appears to apply with more general
(and even matricial) coefficients. It shows that up to a universal
constant all moments of the norm of a linear combination of the form
$$S=\sum\nolimits_j a_j U_j \otimes \bar U_j (1-P)$$
are dominated by those of the corresponding Gaussian sum
$$S'=\sum\nolimits_j a_j Y_j \otimes \bar Y'_j .$$
The advantage is that $S'$ is now simply separately a Gaussian random
variable with respect to the independent Gaussian random matrices $(Y_j)$
and $(Y'_j)$, and hence is much easier to majorize. Note we plan to
incorporate this appendix into our future publication.
Archive classification: math.OA
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.1055
or
http://arXiv.org/abs/1211.1055
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Bernd Carl, Aicke Hinrichs, and Philipp Rudolph
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:32:20 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Entropy numbers of convex hulls
in Banach spaces and applications" by Bernd Carl, Aicke Hinrichs, and
Philipp Rudolph.
Abstract: Entropy numbers and Kolmogorov numbers of convex hulls in
Banach spaces are studied. Applications are given.
Archive classification: math.FA
Mathematics Subject Classification: 41A46, 46B20, 47B06, 46B50
Submitted from: a.hinrichs at uni-jena.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.1559
or
http://arXiv.org/abs/1211.1559
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pawel Wolff
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:34:20 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On randomness reduction in the
Johnson-Lindenstrauss lemma" by Pawel Wolff.
Abstract: A refinement of so-called fast Johnson-Lindenstrauss
transform, due to Ailon and Chazelle (2006), and Matou\v{s}ek (2008),
is proposed. While it preserves the time efficiency and simplicity of
implementation of the original construction, it reduces randomness
used to generate the random transformation. In the analysis of the
construction two auxiliary results are established which might be
of independent interest: a Bernstein-type inequality for a sum of =
a random sample from a family of independent random variables and a
normal approximation result for such a sum.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60E15, 46B85
Submitted from: pwolff at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1202.5500
or
http://arXiv.org/abs/1202.5500
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joanna Garbulinska
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:36:09 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isometric uniqueness of a
complementably universal Banach space for Schauder decompositions"
by Joanna Garbulinska.
Abstract: We present an isometric version of the complementably universal
Banach space $\mathbb{P}$ with a Schauder decomposition. The space
$\mathbb{P}$ is isomorphic to Pe\l czy\'nski's space with a universal
basis as well as to Kadec' complementably universal space with the
bounded approximation property.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46B04. Secondary:46M15, 46M40
Submitted from: jgarbulinska at ujk.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.2211
or
http://arXiv.org/abs/1211.2211
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez, Nikos Dafnis, Maria A. Hernandez Cifre, and Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:38:28 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On mean outer radii of random
polytopes" by David Alonso-Gutierrez, Nikos Dafnis, Maria A. Hernandez
Cifre, and Joscha Prochno.
Abstract: In this paper we introduce a new sequence of quantities
for random polytopes. Let $K_N=\conv\{X_1,\dots,X_N\}$ be a
random polytope generated by independent random vectors uniformly
distributed in an isotropic convex body $K$ of $\R^n$. We prove that
the so-called $k$-th mean outer radius $\widetilde R_k(K_N)$ has order
$\max\{\sqrt{k},\sqrt{\log N}\}L_K$ with high probability if $n^2\leq
N\leq e^{\sqrt{n}}$. We also show that this is also the right order of
the expected value of $\widetilde R_k(K_N)$ in the full range $n\leq
N\leq e^{\sqrt{n}}$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 52A22, Secondary 52A23, 05D40
Remarks: 14 pages
Submitted from: prochno at math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.2336
or
http://arXiv.org/abs/1211.2336
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by William B. Johnson and Sofia Ortega Castillo
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:40:10 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The cluster value problem in spaces
of continuous functions" by William B. Johnson and Sofia Ortega Castillo.
Abstract: We study the cluster value problem for certain Banach algebras
of holomorphic functions defined on the unit ball of a complex Banach
space X. The main results are for spaces of the form X = C(K).
Archive classification: math.FA math.CV
Mathematics Subject Classification: Several complex variables and analytic
spaces, Functional
Submitted from: ortega at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.2339
or
http://arXiv.org/abs/1211.2339
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:44:11 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A reflexive space whose algebra
of operators is not a Grothendieck" by Tomasz Kania.
Abstract: By a result of Johnson, the Banach space
$F=(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_\infty}$ contains a
complemented copy of $\ell_1$. We identify $F$ with a complemented
subspace of the space of (bounded, linear) operators on the reflexive
space $(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_p}$ ($p\in (1,\infty))$,
thus giving a negative answer to the problem posed in the monograph of
Diestel and Uhl which asks whether the space of operators on a reflexive
Banach space is Grothendieck.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46B25, 47L10
Submitted from: t.kania at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.2867
or
http://arXiv.org/abs/1211.2867
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ludek Zajicek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:47:11 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Gateaux and Hadamard
differentiability via directional differentiability" by Ludek Zajicek.
Abstract: Let $X$ be a separable Banach space, $Y$ a Banach space and
$f: X \to Y$ an arbitrary mapping. Then the following implication holds
at each point $x \in X$ except a $\sigma$-directionally porous set:\
If the one-sided Hadamard directional derivative $f'_{H+}(x,u)$ exists
in all directions $u$ from a set $S_x \subset X$ whose linear span is
dense in $X$, then $f$ is Hadamard differentiable at $x$.
This theorem improves and generalizes a recent result of A.D. Ioffe,
in which the linear span of $S_x$ equals $X$ and $Y = \R$. An analogous
theorem, in which $f$ is pointwise Lipschitz, and which deals with the
usual one-sided derivatives and G\^ ateaux differentiability is also
proved. It generalizes a result of D. Preiss and the author, in which $f$
is supposed to be Lipschitz.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46G05, Secondary: 26B05,
49J50
Submitted from: zajicek at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.2604
or
http://arXiv.org/abs/1211.2604
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pawel Kolwicz, Karol Lesnik and Lech Maligranda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:51:52 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Pointwise products of some Banach
function spaces and factorization" by Pawel Kolwicz, Karol Lesnik and
Lech Maligranda.
Abstract: The well-known factorization theorem of Lozanovski{\u \i} may be
written in the form $L^{1}\equiv E\odot E^{\prime }$, where $\odot $ means
the pointwise product of Banach ideal spaces. A natural generalization
of this problem would be the question when one can factorize $F$ through
$E$, i.e., when $F\equiv E\odot M(E, F) \,$, where $M(E, F) $ is the
space of pointwise multipliers from $E$ to $F$. Properties of $M(E, F) $
were investigated in our earlier paper [KLM12] and here we collect and
prove some properties of the construction $E\odot F$. The formulas for
pointwise product of Calder\'{o}n-Lozanovski{\u \i} $E_{\varphi}$ spaces,
Lorentz spaces and Marcinkiewicz spaces are proved. These results are
then used to prove factorization theorems for these spaces. Finally,
it is proved in Theorem 11 that under some natural assumptions, a
rearrangement invariant Banach function space may be factorized through
Marcinkiewicz space.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B42, 46A45
Remarks: 43 pages
Submitted from: lech.maligranda at ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.3135
or
http://arXiv.org/abs/1211.3135
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christina Brech and Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:53:13 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$\ell_\infty$-sums and the Banach
space $\ell_\infty/c_0$" by Christina Brech and Piotr Koszmider.
Abstract: We prove that the use of the Continuum Hypothesis in
some results of Drewnowski and Roberts concerning the Banach space
$\ell_\infty/c_0$ cannot be avoided. In particular, we prove that
in the $\omega_2$-Cohen model, $\ell_\infty(c_0(\mathfrak{c}))$ does
not embed isomorphically into $\ell_\infty/c_0$ where $\mathfrak{c}$
is the cardinality of the continuum. It follows that consistently
$\ell_\infty/c_0$ is not isomorphically of the form $\ell_\infty(X)$
for any Banach space $X$.
Archive classification: math.FA math.LO
Submitted from: christina.brech at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.3173
or
http://arXiv.org/abs/1211.3173
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Costas Poulios
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 Nov 2012 10:54:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The fixed point property in a
Banach space isomorphic to $c_0$" by Costas Poulios.
Abstract: We consider a Banach space, which comes naturally from c0 and
it appears in the literature, and we prove that this space has the fixed
point property for non-expansive mappings.
Archive classification: math.FA
Submitted from: k-poulios at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.3335
or
http://arXiv.org/abs/1211.3335
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Itai Ben Yaacov and C. Ward Henson
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:12:26 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Generic orbits and type isolation
in the Gurarij space" by Itai Ben Yaacov and C. Ward Henson.
Abstract: We study model-theoretic aspects of the separable Gurarij
space $\bG$, in particular type isolation and the existence of prime
models, without use of formal logic. \begin{enumerate} \item If $E$
is a finite-dimensional Banach space, then the set of isolated types
over $E$ is dense, and there exists a prime Gurarij over $E$. This is
the unique separable Gurarij space $\bG$ extending $E$ with the unique
Hahn-Banach extension property (\emph{property $U$}), and the orbit
of $\id\colon E \hookrightarrow \bG$ under the action of $\Aut(\bG)$
is a dense $G_\delta$ in the space of all linear isometric embeddings
$E \hookrightarrow \bG$. \item If $E$ is infinite-dimensional then there
are no non realised isolated types, and therefore no prime model over $E$
(unless $\bG \cong E$), and all orbits of embeddings $E \hookrightarrow
\bG$ are meagre. On the other hand, there are Gurarij spaces extending
$E$ with property $U$. \end{enumerate} We also point out that the class
of Gurarij space is the class of models of an $\aleph_0$-categorical
theory with quantifier elimination, and calculate the density character
of the space of types over $E$, answering a question of Avil\'es et al.
Archive classification: math.FA math.LO
Submitted from: begnac.arxiv at free.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.4814
or
http://arXiv.org/abs/1211.4814
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Claudia Correa and Daniel V. Tausk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:13:45 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On extensions of $c_0$-valued
operators" by Claudia Correa and Daniel V. Tausk.
Abstract: We study pairs of Banach spaces $(X,Y)$, with $Y\subset X$,
for which the thesis of Sobczyk's theorem holds, namely, such that every
bounded $c_0$-valued operator defined in $Y$ extends to $X$. In this
case, we say that $Y$ has the $c_0$-extension property in $X$. We are
mainly concerned with the case when $X$ is a $C(K)$ space and $Y\equiv
C(L)$ is a Banach subalgebra of $C(K)$. The main result of the article
states that, if $K$ is a compact line and $L$ is countable, then $C(L)$
has the $c_0$-extension property in $C(K)$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46E15, 54F05
Remarks: 16 pages
Submitted from: tausk at ime.usp.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.4830
or
http://arXiv.org/abs/1211.4830
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by V. Mykhaylyuk, M. Popov, B.
Randrianantoanina, and G. Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:16:04 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Narrow and $\ell_2$-strictly
singular operators from $L_p$" by V. Mykhaylyuk, M. Popov,
B. Randrianantoanina, and G. Schechtman.
Abstract: In the first part of the paper we prove that for $2 < p, r <
\infty$ every operator $T: L_p \to \ell_r$ is narrow. This completes the
list of sequence and function Lebesgue spaces $X$ with the property that
every operator $T:L_p \to X$ is narrow.
Next, using similar methods we prove that every $\ell_2$-strictly
singular operator from $L_p$, $1<p<\infty$, to any Banach space with an
unconditional basis, is narrow, which partially answers a question of
Plichko and Popov posed in 1990.
A theorem of H.~P.~Rosenthal asserts that if an operator $T$ on
$L_1[0,1]$ satisfies the assumption that for each measurable set $A
\subseteq [0,1]$ the restriction $T \bigl|_{L_1(A)}$ is not an isomorphic
embedding, then $T$ is narrow. (Here $L_1(A) = \{x \in L_1: {\rm supp}
\, x \subseteq A\}$.) Inspired by this result, in the last part of the
paper, we find a sufficient condition, of a different flavor than being
$\ell_2$-strictly singular, for operators on $L_p[0,1]$, $1<p<2$, to be
narrow. We define a notion of a ``gentle'' growth of a function and we
prove that for $1 < p < 2$ every operator $T$ on $L_p$ which, for every
$A\subseteq[0,1]$, sends a function of ``gentle" growth supported on $A$
to a function of arbitrarily small norm is narrow.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47B07, secondary 47B38,
46B03, 46E30
Remarks: Dedicated to the memory of Joram Lindenstrauss
Submitted from: randrib at muohio.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.4854
or
http://arXiv.org/abs/1211.4854
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ruidong Wang, Xujian Huang, and Dongni Tan
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:17:53 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the numerical radius of
Lipschitz operators in Banach spaces" by Ruidong Wang, Xujian Huang,
and Dongni Tan.
Abstract: We study the numerical radius of Lipschitz operators on Banach
spaces via the Lipschitz numerical index, which is an analogue of the
numerical index in Banach space theory. We give a characterization of
the numerical radius and obtain a necessary and sufficient condition for
Banach spaces to have Lipschitz numerical index $1$. As an application,
we show that real lush spaces and $C$-rich subspaces have Lipschitz
numerical index $1$. Moreover, using the G$\hat{a}$teaux differentiability
of Lipschitz operators, we characterize the Lipschitz numerical index of
separable Banach spaces with the RNP. Finally, we prove that the Lipschitz
numerical index has the stability properties for the $c_0$-, $l_1$-, and
$l_\infty$-sums of spaces and vector-valued function spaces. From this,
we show that the $C(K)$ spaces, $L_1(\mu)$-spaces and $L_\infty(\nu)$
spaces have Lipschitz numerical index $1$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, secondary 47A12
Remarks: 23 pages
Submitted from: huangxujian86 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.5753
or
http://arXiv.org/abs/1211.5753
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kallol Paul, Debmalya Sain and Kanhaiya Jha
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:21:43 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On strong orthogonality and
strictly convex normed linear spaces" by Kallol Paul, Debmalya Sain and
Kanhaiya Jha.
Abstract: We introduce the notion of strongly orthogonal set relative to
an element in the sense of Birkhoff-James in a normed linear space to
find a necessary and sufficient condition for an element $ x $ of the
unit sphere $ S_{X}$ to be an exposed point of the unit ball $ B_X .$
We then prove that a normed linear space is strictly convex iff for each
element x of the unit sphere there exists a bounded linear operator A
on X which attains its norm only at the points of the form $ \lambda x $
with $ \lambda \in S_{K} $.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 47A30
Submitted from: kalloldada at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.6489
or
http://arXiv.org/abs/1211.6489
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Silvia Lassalle and Pablo Turco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:22:51 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Operators ideals and approximation
properties" by Silvia Lassalle and Pablo Turco.
Abstract: We use the notion of $\A$-compact sets, which are determined
by a Banach operator ideal $\A$, to show that most classic results of
certain approximation properties and several Banach operator ideals can
be systematically studied under this framework. We say that a Banach
space enjoys the $\A$-approximation property if the identity map is
uniformly approximable on $\A$-compact sets by finite rank operators. The
Grothendieck's classic approximation property is the $\K$-approximation
property for $\K$ the ideal of compact operators and the $p$-approximation
property is obtained as the $\mathcal N^p$-approximation property for
$\mathcal N^p$ the ideal of right $p$-nuclear operators. We introduce
a way to measure the size of $\A$-compact sets and use it to give
a norm on $\K_\A$, the ideal of $\A$-compact operators. Most of our
results concerning the operator Banach ideal $\K_\A$ are obtained for
right-accessible ideals $\A$. For instance, we prove that $\K_\A$ is a
dual ideal, it is regular and we characterize its maximal hull. A strong
concept of approximation property, which makes use of the norm defined
on $\K_\A$, is also addressed. Finally, we obtain a generalization of
Schwartz theorem with a revisited $\epsilon$-product.
Archive classification: math.FA
Mathematics Subject Classification: 46G20, 46B28, 47B07
Remarks: 22 Pages
Submitted from: paturco at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1211.7366
or
http://arXiv.org/abs/1211.7366
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anil Kumar Karn
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:24:50 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Orthogonality in $\ell _p$-spaces
and its bearing on ordered Banach spaces" by Anil Kumar Karn.
Abstract: We introduce a notion of $p$-orthogonality in a general Banach
space $1 \le p \le \infty$. We use this concept to characterize $\ell
_p$-spaces among Banach spaces and also among complete order smooth
$p$-normed spaces. We further introduce a notion of $p$-orthogonal
decomposition in order smooth $p$-normed spaces. We prove that if the
$\infty$-orthogonal decomposition holds in an order smooth $\infty$-normed
space, then the $1$-orthogonal decomposition holds in the dual space. We
also give an example to show that the above said decomposition may not
be unique.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46B40, Secondary: 46B45,
47B60
Submitted from: anilkarn at niser.ac.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.0054
or
http://arXiv.org/abs/1212.0054
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergey V. Astashkin and Lech Maligranda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:26:17 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A short proof of some recent
results related to Ces{\`a}ro function spaces" by Sergey V. Astashkin
and Lech Maligranda.
Abstract: We give a short proof of the recent results that, for every
$1\leq p< \infty,$ the Ces{\`a}ro function space $Ces_p(I)$ is not a
dual space, has the weak Banach-Saks property and does not have the
Radon-Nikodym property.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B42
Remarks: 4 pages
Submitted from: lech.maligranda at ltu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.0346
or
http://arXiv.org/abs/1212.0346
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando and Pablo Sevilla-Peris
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:27:38 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Extendibility of bilinear forms
on Banach sequence spaces" by Daniel Carando and Pablo Sevilla-Peris.
Abstract: We study Hahn-Banach extensions of multilinear forms defined
on Banach sequence spaces. We characterize $c_0$ in terms of extension
of bilinear forms, and describe the Banach sequence spaces in which
every bilinear form admits extensions to any superspace.
Archive classification: math.FA
Submitted from: dcarando at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.0777
or
http://arXiv.org/abs/1212.0777
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jose Bonet, Carmen Fernandez, Antonio
Galbis, and Juan M. Ribera
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:29:24 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Shrinking and boundedly complete
atomic decompositions in Fr\'echet spaces" by Jose Bonet, Carmen
Fernandez, Antonio Galbis, and Juan M. Ribera.
Abstract: We study atomic decompositions in Fr\'echet spaces and
their duals, as well as perturbation results. We define shrinking and
boundedly complete atomic decompositions on a locally convex space,
study the duality of these two concepts and their relation with the
reflexivity of the space. We characterize when an unconditional atomic
decomposition is shrinking or boundedly complete in terms of properties
of the space. Several examples of concrete atomic decompositions in
function spaces are also presented.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46A04, secondary: 42C15
Submitted from: antonio.galbis at uv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.0969
or
http://arXiv.org/abs/1212.0969
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pierre Youssef
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:34:59 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on column subset selection"
by Pierre Youssef.
Abstract: Given a matrix U, using a deterministic method, we extract a
"large" submatrix of U'(whose columns are obtained by normalizing those
of U) and estimate its smallest and largest singular value. We apply
this result to the study of contact points of the unit ball with its
maximal volume ellipsoid. We consider also the paving problem and give a
deterministic algorithm to partition a matrix into almost isometric blocks
recovering previous results of Bourgain-Tzafriri and Tropp. Finally,
we partially answer a question raised by Naor about finding an algorithm
in the spirit of Batson-Spielman-Srivastava's work to extract a "large"
square submatrix of "small" norm.
Archive classification: math.FA
Remarks: 12 pages
Submitted from: pierre.youssef at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.0976
or
http://arXiv.org/abs/1212.0976
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vincent Lafforgue and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:36:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Vertical versus horizontal
Poincar\'e inequalities on the Heisenberg group" by Vincent Lafforgue
and Assaf Naor.
Abstract: Let $\H= \left\langle a,b\,|\, a[a,b]=[a,b]a\ \wedge\
b[a,b]=[a,b]b\right\rangle$ be the discrete Heisenberg group, equipped
with the left-invariant word metric $d_W(\cdot,\cdot)$ associated to
the generating set $\{a,b,a^{-1},b^{-1}\}$. Letting $B_n= \{x\in \H:\
d_W(x,e_\H)\le n\}$ denote the corresponding closed ball of radius
$n\in \N$, and writing $c=[a,b]=aba^{-1}b^{-1}$, we prove that if
$(X,\|\cdot\|_X)$ is a Banach space whose modulus of uniform convexity has
power type $q\in [2,\infty)$ then there exists $K\in (0,\infty)$ such that
every $f:\H\to X$ satisfies \begin{multline*} \sum_{k=1}^{n^2}\sum_{x\in
B_n}\frac{ \|f(xc^k)-f(x)\|_X^q}{k^{1+q/2}}\\\le K\sum_{x\in B_{21n}}
\Big(\|f(xa)-f(x)\|^q_X+\|f(xb)-f(x)\|^q_X\Big). \end{multline*} It
follows that for every $n\in \N$ the bi-Lipschitz distortion of every
$f:B_n\to X$ is at least a constant multiple of $(\log n)^{1/q}$, an
asymptotically optimal estimate as $n\to\infty$.
Archive classification: math.MG math.FA math.GR
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.2107
or
http://arXiv.org/abs/1212.2107
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jaegil Kim
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:38:10 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Minimal volume product near Hanner
polytopes" by Jaegil Kim.
Abstract: Mahler's conjecture asks whether the cube is a minimizer for the
volume product of a body and its polar in the class of symmetric convex
bodies in a fixed dimension. It is known that every Hanner polytope
has the same volume product as the cube or the cross-polytope. In this
paper we prove that every Hanner polytope is a strict local minimizer
for the volume product in the class of symmetric convex bodies endowed
with the Banach-Mazur distance.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A20, 52A40, 52B11
Submitted from: jkim at math.kent.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.2544
or
http://arXiv.org/abs/1212.2544
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vladimir P. Fonf, Michael Levin and
Clemente Zanco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:39:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Covering $L^p$ spaces by balls"
by Vladimir P. Fonf, Michael Levin and Clemente Zanco.
Abstract: We prove that, given any covering of any separable
infinite-dimensional uniformly rotund and uniformly smooth Banach space
$X$ by closed balls each of positive radius, some point exists in $X$
which belongs to infinitely many balls.
Archive classification: math.FA math.GN
Mathematics Subject Classification: Primary 46B20, Secondary 54D20
Submitted from: mlevine at cs.bgu.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.2817
or
http://arXiv.org/abs/1212.2817
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yoav Kallus and Fedor Nazarov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:40:39 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "In which dimensions is the ball
relatively worst packing?" by Yoav Kallus and Fedor Nazarov.
Abstract: It was conjectured by Ulam that the ball has the lowest
optimal lattice packing density out of all convex, origin-symmetric
three-dimensional solids. We affirm a local version of this conjecture:
the ball has a lower optimal lattice packing than any body of sufficiently
small asphericity in three dimensions. We also show that in dimensions
4, 5, 6, 7, 8, and 24 there are bodies of arbitrarily small asphericity
that pack worse than balls.
Archive classification: math.MG cond-mat.soft math.FA
Remarks: 15 pages, 1 figure
Submitted from: ykallus at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.2551
or
http://arXiv.org/abs/1212.2551
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jean Bourgain
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 17 Dec 2012 14:41:57 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Hardy-Littlewood maximal
function for the cube" by Jean Bourgain.
Abstract: It is shown that the Hardy-Littlewood maximal function
associated to the cube in $\mathbb R^n$ obeys dimensional free bounds
in $L^p$ fir $p>1$. Earlier work only covered the range $p>\frac 32$.
Archive classification: math.FA
Mathematics Subject Classification: 42B25
Remarks: 20 pages
Submitted from: bourgain at ias.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1212.2661
or
http://arXiv.org/abs/1212.2661
Return-path: <alspach at math.okstate.edu>
Subject: Sad News
From: Dale Alspach <alspach at szlenk.math.okstate.edu>
Date: Thu, 20 Dec 2012 07:00:05 -0600
To: banach
Today, December 20 in the morning, after prolonged illness, died Aleksander
Pelczynski, one of the founding fathers of modern Banach space theory.
P. Wojtaszczyk
Interdyscyplinarne Centrum Modelowania Matematycznego i Komputerowego
Uniwersytet Warszawski,
Ul. Prosta 69 second floor
00-838 Warszawa
Return-path: <alspach at math.okstate.edu>
Subject: Lindenstrauss' memorial conference
From: Dale Alspach <alspachde at gmail.com>
To: banach at math.okstate.edu
Date: Mon, 31 Dec 2012 17:03:59 -0600
---------- Forwarded message ----------
From: "Tomek Szankowski" <tomek.szankowski at mail.huji.ac.il>
The Hebrew University is organizing a memorial conference for Joram
Lindenstrauss.
The conference, titled " Banach Spaces: Geometry and Analysis "
will be held in Jerusalem , May 26-31, 2013.
Participation is open to all.
The site of the conference (containing the main speakers' list and the
registration form) is
http://www.as.huji.ac.il/content/banach-spaces-geometry-and-analysis-0
Tomek Szankowski
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