Messages from 2014
These are the messages distributed to the Banach list during 2014.
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 4 Jan 2014 15:10:12 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Metric characterizations of
superreflexivity in terms of word groups and finite graphs" by Mikhail
Ostrovskii.
Abstract: We show that superreflexivity can be characterized in terms
of bilipschitz embeddability of word hyperbolic groups. We compare
characterizations of superreflexivity in terms of diamond graphs and
binary trees. We show that there exist sequences of series-parallel
graphs of increasing topological complexity which admit uniformly
bilipschitz embeddings into a Hilbert space, and thus do not characterize
superreflexivity.
Archive classification: math.MG math.CO math.FA math.GR
Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12,
20F67, 46B07
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.4627
or
http://arXiv.org/abs/1312.4627
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: Sat, 4 Jan 2014 15:12:15 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Finite forms of Gowers' theorem
on the oscillation stability of $c_0$" by Diana Ojeda-Aristizabal.
Abstract: We give a constructive proof of the finite version of Gowers'
$FIN_k$ Theorem and analyse the corresponding upper bounds. The $FIN_k$
Theorem is closely related to the oscillation stability of $c_0$. The
stabilization of Lipschitz functions on arbitrary finite dimensional
Banach spaces was studied well before by V. Milman. We compare the finite
$FIN_k$ Theorem with the finite stabilization principle in the case of
spaces of the form $\ell_{\infty}^n$, $n\in\mathbb{N}$ and establish a
much slower growing upper bound for the finite stabilization principle
in this particular case.
Archive classification: math.CO math.FA
Mathematics Subject Classification: 05D10
Remarks: 18 pages
Submitted from: dco34 at cornell.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.4639
or
http://arXiv.org/abs/1312.4639
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mohammad N. Ivaki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 4 Jan 2014 15:14:19 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The planar Busemann-Petty centroid
inequality and its stability" by Mohammad N. Ivaki.
Abstract: In [Centro-affine invariants for smooth convex bodies,
Int. Math. Res. Notices. doi: 10.1093/imrn/rnr110, 2011] Stancu
introduced a family of centro-affine normal flows, $p$-flow, for $1\leq
p<\infty.$ Here we investigate the asymptotic behavior of the planar
$p$-flow for $p=\infty$, in the class of smooth, origin-symmetric convex
bodies. The motivation is the Busemann-Petty centroid inequality. First,
we prove that the $\infty$-flow evolves appropriately normalized
origin-symmetric solutions to the unit disk in the Hausdorff metric,
modulo $SL(2).$ Second, as an application of this weak convergence,
we prove the planar Busemann-Petty centroid inequality in the of class
convex bodies having the origin of the plane in their interiors. Third,
using the $\infty$-flow, we prove a stability version of the planar
Busemann-Petty centroid inequality, in the Banach-Mazur distance, in
the class of origin-symmetric convex bodies. Fourth, we prove that the
convergence in the Hausdorff metric can be improved to convergence in
the $\mathcal{C}^{\infty}$ topology.
Archive classification: math.DG math.FA
Mathematics Subject Classification: Primary 52A40, 53C44, 52A10, Secondary
35K55, 53A15
Remarks: Two preprints unified into one
Submitted from: mohammad.ivaki at tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.4834
or
http://arXiv.org/abs/1312.4834
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 4 Jan 2014 15:16:10 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Metric spaces nonembeddable
into Banach spaces with the property and thick families of geodesics"
by Mikhail Ostrovskii.
Abstract: We show that a geodesic metric space which does not admit
bilipschitz embeddings into Banach spaces with the Radon-Nikod\'ym
property does not necessarily contain a bilipschitz image of a thick
family of geodesics. This is done by showing that any thick family of
geodesics is not Markov convex, and comparing this result with results of
Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier
result of the author that any Banach space without the Radon-Nikod\'ym
property contains a bilipschitz image of a thick family of geodesics.
Archive classification: math.MG math.FA
Mathematics Subject Classification: Primary 30L05, Secondary: 46B22, 46B85
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.5381
or
http://arXiv.org/abs/1312.5381
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Koldobsky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 4 Jan 2014 15:19:07 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A hyperplane inequality for
measures of unconditional convex bodies" by Alexander Koldobsky.
Abstract: We prove an inequality that extends to arbitrary measures
the hyperplane inequality for volume of unconditional convex bodies
originally observed by Bourgain.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 52A20
Submitted from: koldobskiya at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.7048
or
http://arXiv.org/abs/1312.7048
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sun Kwang Kim, Han Ju Lee and Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 4 Jan 2014 15:21:06 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the Bishop-Phelps-Bollobas
property for numerical radius" by Sun Kwang Kim, Han Ju Lee and Miguel
Martin.
Abstract: We study the Bishop-Phelps-Bollob\'as property for numerical
radius (in short, BPBp-$\nuu$) and find sufficient conditions for
Banach spaces ensuring the BPBp-$\nuu$. Among other results, we show
that $L_1(\mu)$-spaces have this property for every measure $\mu$. On
the other hand, we show that every infinite-dimensional separable Banach
space can be renormed to fail the BPBp-$\nuu$. In particular, this shows
that the Radon-Nikod\'{y}m property (even reflexivity) is not enough to
get BPBp-$\nuu$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Submitted from: hanjulee at dongguk.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.7698
or
http://arXiv.org/abs/1312.7698
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Fresen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 4 Jan 2014 15:23:24 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Explicit Euclidean embeddings in
permutation invariant normed spaces" by Daniel Fresen.
Abstract: Let $(X,\left\Vert \cdot \right\Vert )$ be a real normed
space of dimension $N\in \mathbb{N}$ with a basis $(e_{i})_{1}^{N}$
such that the norm is invariant under coordinate permutations. Assume
for simplicity that the basis constant is at most $2$. Consider any $n\in
\mathbb{N}$ and $0<\varepsilon <1/4$ such that $n\leq c(\log \varepsilon
^{-1})^{-1}\log N$. We provide an explicit construction of a matrix that
generates a $(1+\varepsilon )$ embedding of $\ell _{2}^{n}$ into $X$.
Archive classification: math.FA
Mathematics Subject Classification: 46B06, 46B07, 52A20, 52A21, 52A23
Remarks: 14 pages
Submitted from: daniel.fresen at yale.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.0203
or
http://arXiv.org/abs/1401.0203
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D. Carando, S. Lassalle, and M. Mazzitelli
From: alspach at math.okstate.edu (Dale Alspach)
Date: Sat, 4 Jan 2014 15:25:44 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A Lindenstrauss theorem for
some classes of multilinear mappings" by D. Carando, S. Lassalle, and
M. Mazzitelli.
Abstract: Under some natural hypotheses, we show that if a multilinear
mapping belongs to some Banach multlinear ideal, then it can be
approximated by multilinear mappings belonging to the same ideal whose
Arens extensions simultaneously attain their norms. We also consider
the class of symmetric multilinear mappings.
Archive classification: math.FA
Remarks: 11 pages
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/1401.0488
or
http://arXiv.org/abs/1401.0488
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Geometry of Banach Spaces - A conference in honor of
Stanimir Troyanski
From: Jose Rodriguez <joserr at um.es>
Date: Wed, 15 Jan 2014 11:44:57 +0100
To: banach at math.okstate.edu
Dear colleagues:
This is the second announcement of the conference
Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski
which will be held in Albacete (Spain) on June 10-13, 2014, on the
occasion of the 70th birthday of Professor Troyanski.
Our web page at
https://sites.google.com/site/geometryofbanachspaces/
contains detailed information about the conference.
Main speakers who accepted our invitation are: S. Argyros, J. Castillo,
S. Dilworth, M. Fabian, V. Fonf, G. Godefroy, P. Hajek, R. Haydon, F.
Hernandez, P. Kenderov, P. Koszmider, D. Kutzarova, V. Milman, A. Molto,
T. Schlumprecht, R. Smith, A. Suarez Granero.
Registration is OPEN. Participants must pay a fee which will cover
conference materials, lunches and coffee breaks during the conference.
Details about the payment can be found in our web page.
- Deadline for early registration: April 30.
- Deadline for late registration: May 31.
Participants will have the opportunity to deliver a short talk. The
deadline for abstract submission is May 15.
Accommodation: the conference web page includes a list of hotels in
Albacete offering special rates for the participants.
Please do not hesitate in contacting us at
geometry.banach.spaces.2014 at gmail.com if you need further information.
Looking forward to meeting you!
The organizers,
A. Aviles, S. Lajara, J.P. Moreno, J. Rodriguez.
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
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Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fernando Albiac and Jose L. Ansorena
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:36:03 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Non-existence of greedy bases
in direct sums of mixed $\ell_{p}$ spaces" by Fernando Albiac and Jose
L. Ansorena.
Abstract: The fact that finite direct sums of two or more mutually
different spaces from the family $\{\ell_{p} : 1\le p<\infty\}\cup c_{0}$
fail to have greedy bases is stated in [Dilworth et al., Greedy bases
for Besov spaces, Constr. Approx. 34 (2011), no. 2, 281-296]. However,
the concise proof that the authors give of this fundamental result
in greedy approximation relies on a fallacious argument, namely the
alleged uniqueness of unconditional basis up to permutation of the
spaces involved. The main goal of this note is to settle the problem by
providing a correct proof. For that we first show that all greedy bases
in an $\ell_{p}$ space have fundamental functions of the same order. As
a by-product of our work we obtain that {\it every} almost greedy basis
of a Banach space with unconditional basis and nontrivial type contains
a greedy subbasis.
Archive classification: math.FA
Mathematics Subject Classification: 41A35, 46B15 46B45, 46T99
Submitted from: joseluis.ansorena at unirioja.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.0693
or
http://arXiv.org/abs/1401.0693
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Wilson Cuellar-Carrera
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:37:55 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A Banach space with a countable
infinite number of complex structures" by Wilson Cuellar-Carrera.
Abstract: We give examples of real Banach spaces with exactly infinite
countably many complex structures and with $\omega_1$ many complex
structures.
Archive classification: math.FA
Submitted from: cuellar at ime.usp.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.1781
or
http://arXiv.org/abs/1401.1781
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dale E. Alspach and Eloi Medina Galego
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:40:36 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A complete classification of
the spaces of compact operators on C([1,alpha], l_p) spaces, 1<p<
infinity" by Dale E. Alspach and Eloi Medina Galego.
Abstract: We complete the classification, up to isomorphism, of the spaces
of compact operators on C([1, gamma], l_p) spaces, 1<p< infinity. In
order to do this, we classify, up to isomorphism, the spaces of compact
operators {\mathcal K}(E, F), where E= C([1, lambda], l_p) and F=C([1,xi],
l_q) for arbitrary ordinals lambda and xi and 1< p \leq q< infinity.
More precisely, we prove that it is relatively consistent with ZFC
that for any infinite ordinals lambda, mu, xi and eta the following
statements are equivalent:
(a) {\mathcal K}(C([1, lambda], l_p), C([1, xi], l_q)) is isomorphic to
{\mathcal K}(C([1, mu], l_p), C([1, eta], l_q)) .
(b) lambda and mu have the same cardinality and C([1,xi]) is
isomorphic to C([1, eta]) or there exists an uncountable regular ordinal
alpha and 1 \leq m, n < omega such that C([1, xi]) is isomorphic to C([1,
alpha m]) and C([1,eta]) is isomorphic to C([1, alpha n]).
Moreover, in ZFC, if lambda and mu are finite ordinals and xi and
eta are infinite ordinals then the statements (a) and (b') are equivalent.
(b') C([1,xi]) is isomorphic to C([1, eta]) or there exists an
uncountable regular ordinal alpha and 1 \leq m, n \leq omega such that
C([1, xi]) is isomorphic to C([1, alpha m]) and C([1,eta]) is isomorphic
to C([1, alpha n]).
Archive classification: math.FA
Mathematics Subject Classification: 46B03 (primary) 46B25 (secondary)
Remarks: Revised version will appear in Proc. AMS
Submitted from: alspach at math.okstate.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.1857
or
http://arXiv.org/abs/1401.1857
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Andrzej Wisnicki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:42:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Hyper-extensions in metric fixed
point theory" by Andrzej Wisnicki.
Abstract: We apply a modern axiomatic system of nonstandard analysis in
metric fixed point theory. In particular, we formulate a nonstandard
iteration scheme for nonexpansive mappings and present a nonstandard
approach to fixed-point problems in direct sums of Banach spaces.
Archive classification: math.FA math.LO
Remarks: 12 pages
Submitted from: awisnic at hektor.umcs.lublin.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.2144
or
http://arXiv.org/abs/1401.2144
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dusan Repovs and Pavel V. Semenov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:44:30 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Continuous selections of
multivalued mappings" by Dusan Repovs and Pavel V. Semenov.
Abstract: This survey covers in our opinion the most important
results in the theory of continuous selections of multivalued mappings
(approximately) from 2002 through 2012. It extends and continues our
previous such survey which appeared in Recent Progress in General
Topology, II, which was published in 2002. In comparison, our present
survey considers more restricted and specific areas of mathematics. Note
that we do not consider the theory of selectors (i.e. continuous choices
of elements from subsets of topological spaces) since this topics is
covered by another survey in this volume.
Archive classification: math.GN math.FA math.GT math.OC
Mathematics Subject Classification: 54C60, 54C65, 28B20, 26E25, 49J53,
58C06
Citation: Recent Progress in General Topology III, (K. P. Hart, Jan van
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.2257
or
http://arXiv.org/abs/1401.2257
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tim de Laat and Mikael de la Salle
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:45:55 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strong property (T) for higher
rank simple Lie groups" by Tim de Laat and Mikael de la Salle.
Abstract: We prove that connected higher rank simple Lie groups have
Lafforgue's strong property (T) with respect to a certain class of Banach
spaces $\mathcal{E}_{10}$ containing many classical superreflexive
spaces and some non-reflexive spaces as well. This generalizes the
result of Lafforgue asserting that $\mathrm{SL}(3,\mathbb{R})$ has strong
property (T) with respect to Hilbert spaces and the more recent result
of the second named author asserting that $\mathrm{SL}(3,\mathbb{R})$
has strong property (T) with respect to a certain larger class of
Banach spaces. For the generalization to higher rank groups, it is
sufficient to prove strong property (T) for $\mathrm{Sp}(2,\mathbb{R})$
and its universal covering group. As consequences of our main result,
it follows that for $X \in \mathcal{E}_{10}$, connected higher rank
simple Lie groups and their lattices have property (F$_X$) of Bader,
Furman, Gelander and Monod, and the expanders contructed from a lattice
in such a group do not admit a coarse embedding into $X$.
Archive classification: math.GR math.FA math.MG
Report Number: CPH-SYM-DNRF92
Remarks: 30 pages, 1 figure
Submitted from: tim.delaat at wis.kuleuven.be
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.3611
or
http://arXiv.org/abs/1401.3611
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rainis Haller and Johann Langemets
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:47:38 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometry of Banach spaces with
an octahedral norm" by Rainis Haller and Johann Langemets.
Abstract: We discuss the geometry of Banach spaces whose norm is
octahedral or, more generally, locally or weakly octahedral. Our main
results characterize these spaces in terms of covering of the unit ball.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Submitted from: johann.langemets at ut.ee
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.3612
or
http://arXiv.org/abs/1401.3612
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ian Doust, Stephen Sanchez and Anthony
Weston
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 17 Jan 2014 14:50:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The generalized roundness
of $\ell_\infty^{(3)}$ revisited" by Ian Doust, Stephen Sanchez and
Anthony Weston.
Abstract: Metric spaces of generalized roundness zero have interesting
non-embedding properties. For instance, we note that no metric space of
generalized roundness zero is isometric to any metric subspace of any
$L_{p}$-space for which $0 < p \leq 2$. Lennard, Tonge and Weston gave
an indirect proof that $\ell_{\infty}^{(3)}$ has generalized roundness
zero by appealing to highly non-trivial isometric embedding theorems
of Bretagnolle Dacunha-Castelle and Krivine, and Misiewicz. In this
paper we give a direct proof that $\ell_{\infty}^{(3)}$ has generalized
roundness zero. This provides insight into the combinatorial geometry of
$\ell_{\infty}^{(3)}$ that causes the generalized roundness inequalities
to fail. We complete the paper by noting a characterization of real
quasi-normed spaces of generalized roundness zero.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 8 pages
Submitted from: i.doust at unsw.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.4095
or
http://arXiv.org/abs/1401.4095
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Universality Meeting, Kent State University, April 11-13, 2014
From: Dale Alspach <alspach at math.okstate.edu>
Date: Thu, 23 Jan 2014 14:54:16 -0600
To: banach at math.okstate.edu
Announcing an Informal Analysis Seminar focusing on Universality Friday
afternoon, April 11, 2014 through early Sunday afternoon, April 13, 2014
This meeting has received generous funding from Elsevier, with additional
support from Kent State University. This meeting should be especially
attractive to non-specialists, and in particular to students and
new PhD's. The reason is that the Friday afternoon session is being
devoted to three expository talks, aimed at a non- specialist audience,
on Universality by three excellent speakers: Paul Gauthier (Montreal),
Pamela Gorkin (Bucknell), and Vassili Nestoridis (Athens).
Our speakers on Saturday and Sunday will be Juan Bès, Kit Chan,
Paul Gauthier, Pamela Gorkin, Manuel Maestre, Myrto Manolaki, Vassili
Nestoridis, and Rebecca Sanders.
Also, there is a reasonable possibility of (very) partial support for
students and junior participants.
Registration is free, but we ask intending participants to let us know
of their interest. For further information, please consult:
http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/April_2014.html
and/or contact
Richard Aron at aron at math.kent.edu .
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_______________________________________________
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Subject: [Banach] Integration, Vector Measures and Related Topics VI
From: Grzegorz Plebanek <gplebanek at gmail.com>
Date: Fri, 24 Jan 2014 18:08:30 +0100
To: banach at math.okstate.edu
2nd announcement on the conference
*** Integration, Vector Measures and Related Topics VI
*** June 15 - 21, 2014
*** the Mathematical Research and Conference Center in Bedlewo (near
Poznan, Poland),
Registration and more information on the conference webpage:
http://www.math.uni.wroc.pl/~drygier/ivmrt2014/
Invited speakers: Antonio Aviles (Murcia), Erik J. Balder (Utrecht),
Oscar Blasco (Valencia)
Guillermo Curbera (Sevilla), Luisa Di Piazza (Palermo), Harold Garth
Dales (Lancaster)
Joe Diestel (Kent), Christian Hess (Paris), Marian Fabian (Prague),
David H. Fremlin (Colchester)
Ondrej Kalenda (Prague), Zbigniew Lipecki (Wrocław), Jose Rodriguez
(Murcia)
The organizing committee: M. Balcerzak, M. Cichon, K. Musial, G. Plebanek
_______________________________________________
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Subject: [Banach] Conference Announcement
Date: Sat, 25 Jan 2014 11:17:50 CST
To: banach at math.okstate.edu
From: Krzysztof Jarosz <krzysztof.m.jarosz at gmail.com>
7th Conference on Function Spaces will take place at the SIUE campus
between Ma
y 20 and May 24, 2014:
http://www.siue.edu/MATH/conference2014/
We received an NSF grant to defer travel and local cost primarily for the
parti
cipants without other sources of funding.
Krzysztof Jarosz
Department of Mathematics and Statistics
Southern Illinois University Edwardsville
Edwardsville, IL 62026-1653, USA
tel.: (618) 650-2354
fax: (618) 650-3771
e-mail: kjarosz at siue.edu
http://www.siue.edu/~kjarosz/
_______________________________________________
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Subject: Abstract of a paper by Timur Oikhberg and Eugeniu Spinu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:12:44 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Subprojective Banach spaces"
by Timur Oikhberg and Eugeniu Spinu.
Abstract: A Banach space $X$ is called subprojective if any of its
infinite dimensional subspaces $Y$ contains a further infinite dimensional
subspace complemented in $X$. This paper is devoted to systematic study
of subprojectivity. We examine the stability of subprojectivity of Banach
spaces under various operations, such us direct or twisted sums, tensor
products, and forming spaces of operators. Along the way, we obtain new
classes of subprojective spaces.
Archive classification: math.FA
Submitted from: spinu at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.4231
or
http://arXiv.org/abs/1401.4231
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cesar Ruiz and Victor M. Sanchez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:14:38 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Nonlinear subsets of functions
spaces and spaceability" by Cesar Ruiz and Victor M. Sanchez.
Abstract: In this paper, we study the existence of infinite dimensional
closed linear subspaces of a rearrangement invariant space on [0,1] every
nonzero element of which does not belong to any included rearrangement
invariant space of the same class such that the inclusion operator is
disjointly strictly singular. We consider Lorentz, Marcinkiewicz and
Orlicz spaces. The answer is affirmative for Marcinkiewicz spaces and
negative for Lorentz and Orlicz spaces. Also, the same problem is studied
for Nakano spaces assuming different hypothesis.
Archive classification: math.FA
Mathematics Subject Classification: 46E30
Remarks: 11 pages
Submitted from: victorms at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.5906
or
http://arXiv.org/abs/1401.5906
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pierre Youssef
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:16:35 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Extractig a basis with fixed
block inside a matrix" by Pierre Youssef.
Abstract: Given $U$ an $n\times m$ matrix of rank $n$ and $V$ block
of columns inside $U$, we consider the problem of extracting a block
of columns of rank $n$ which minimize the Hilbert-Schmidt norm of the
inverse while preserving the block $V$. This generalizes a previous
result of Gluskin-Olevskii, and improves the estimates when given a
"good" block $V$.
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/1401.6434
or
http://arXiv.org/abs/1401.6434
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Maria Roginskaya and Michal Wojciechowski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:18:25 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bounded Approximation Property for
Sobolev spaces on simply-connected planar domains" by Maria Roginskaya
and Michal Wojciechowski.
Abstract: We show that Sobolev space $W^1_1(\Omega)$ of any planar
one-connected domain $\Omega$ has the Bounded Approximation property. The
result holds independently from the properties of the boundary of
$\Omega$. The prove is based on a new decomposition of a planar domain.
Archive classification: math.FA
Submitted from: maria.roginskaya at chalmers.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.7131
or
http://arXiv.org/abs/1401.7131
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Umut Caglar and Elisabeth M. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:19:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Mixed f-divergence and inequalities
for log concave functions" by Umut Caglar and Elisabeth M. Werner.
Abstract: Mixed f-divergences, a concept from information theory
and statistics, measure the difference between multiple pairs of
distributions. We introduce them for log concave functions and establish
some of their properties. Among them are affine invariant vector entropy
inequalities, like new Alexandrov-Fenchel type inequalities and an affine
isoperimetric inequality for the vector form of the Kullback Leibler
divergence for log concave functions. Special cases of f-divergences
are mixed L_\lambda-affine surface areas for log concave functions. For
those, we establish various affine isoperimetric inequalities as well
as a vector Blaschke Santalo type inequality.
Archive classification: math.FA
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.7065
or
http://arXiv.org/abs/1401.7065
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Domenico Candeloro and Anna Rita Sambucini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:22:43 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Filter convergence and
decompositions for vector lattice-valued" by Domenico Candeloro and Anna
Rita Sambucini.
Abstract: Filter convergence of vector lattice-valued measures is
considered, in order to deduce theorems of convergence for their
decompositions. First the $\sigma$-additive case is studied, without
particular assumptions on the filter; later the finitely additive case is
faced, first assuming uniform $s$-boundedness (without restrictions on the
filter), then relaxing this condition but imposing stronger properties on
the filter. In order to obtain the last results, a Schur-type convergence
theorem is used.
Archive classification: math.FA
Mathematics Subject Classification: 28B15, 28B05, 06A06, 54F05
Report Number: 0901688 30 jan 2014
Remarks: 18 pages
Submitted from: anna.sambucini at unipg.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.7818
or
http://arXiv.org/abs/1401.7818
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Galicer and Roman Villafane
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:24:46 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Coincidence of extendible
vector-valued ideals with their minimal" by Daniel Galicer and Roman
Villafane.
Abstract: We provide coincidence results for vector-valued ideals of
multilinear operators. More precisely, if $\mathfrak A$ is an ideal of
$n$-linear mappings we give conditions for which the following equality
$\mathfrak A(E_1,\dots,E_n;F) = {\mathfrak A}^{min}(E_1,\dots,E_n;F)$
holds isometrically. As an application, we obtain in many cases
that the monomials form a Schauder basis on the space $\mathfrak
A(E_1,\dots,E_n;F)$. Several structural and geometric properties are also
derived using this equality. We apply our results to the particular
case where $\mathfrak A$ is the classical ideal of extendible or
Pietsch-integral multilinear operators. Similar statements are given
for ideals of vector-valued homogeneous polynomials.
For our purposes we also establish a vector-valued version of the
Littlewood-Bogdanowicz-Pe{\l}czy\'nski theorem, which we believe is
interesting in its own right.
Archive classification: math.FA
Mathematics Subject Classification: 46G25, 46B22, 46M05, 47H60
Remarks: 25 pages
Submitted from: dgalicer at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1401.7896
or
http://arXiv.org/abs/1401.7896
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Asuman G. Aksoy and Grzegorz Lewicki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:26:24 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Minimal projections with respect
to numerical radius" by Asuman G. Aksoy and Grzegorz Lewicki.
Abstract: In this paper we survey some results on minimality of
projections with respect to numerical radius. We note that in the cases
$L^p$, $p=1,2,\infty$, there is no difference between the minimality
of projections measured either with respect to operator norm or with
respect to numerical radius. However, we give an example of a projection
from $l^p_3$ onto a two-dimensional subspace which is minimal with
respect to norm, but not with respect to numerical radius for $p\neq
1,2,\infty$. Furthermore, utilizing a theorem of Rudin and motivated
by Fourier projections, we give a criterion for minimal projections,
measured in numerical radius. Additionally, some results concerning strong
unicity of minimal projections with respect to numerical radius are given.
Archive classification: math.FA
Mathematics Subject Classification: Primary 41A35, 41A65, Secondary 47A12
Remarks: 15 pages
Submitted from: aaksoy at cmc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.0032
or
http://arXiv.org/abs/1402.0032
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuel Milman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:28:18 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the mean-width of isotropic
convex bodies and their associated $L_p$-centroid bodies" by Emanuel
Milman.
Abstract: For any origin-symmetric convex body $K$ in $\mathbb{R}^n$
in isotropic position, we obtain the bound: \[ M^*(K) \leq C \sqrt{n}
\log(n)^2 L_K ~, \] where $M^*(K)$ denotes (half) the mean-width of
$K$, $L_K$ is the isotropic constant of $K$, and $C>0$ is a universal
constant. This improves the previous best-known estimate $M^*(K) \leq C
n^{3/4} L_K$. Up to the power of the $\log(n)$ term and the $L_K$ one, the
improved bound is best possible, and implies that the isotropic position
is (up to the $L_K$ term) an almost $2$-regular $M$-position. The bound
extends to any arbitrary position, depending on a certain weighted average
of the eigenvalues of the covariance matrix. Furthermore, the bound
applies to the mean-width of $L_p$-centroid bodies, extending a sharp
upper bound of Paouris for $1 \leq p \leq \sqrt{n}$ to an almost-sharp
bound for an arbitrary $p \geq \sqrt{n}$. The question of whether it
is possible to remove the $L_K$ term from the new bound is essentially
equivalent to the Slicing Problem, to within logarithmic factors in $n$.
Archive classification: math.FA
Remarks: 14 pages
Submitted from: emanuel.milman at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.0209
or
http://arXiv.org/abs/1402.0209
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jarno Talponen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:29:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "ODE representation for varying
exponent $L^p$ norm" by Jarno Talponen.
Abstract: We will construct Banach function space norms arising as weak
solutions to ordinary differential equations of first order. This provides
as a special case a new way of defining varying exponent $L^p$ spaces,
different from the Orlicz type approach. It turns out that the duality of
these spaces behaves in an anticipated way, same as the uniform convexity
and uniform smoothness.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 46E30, 46B10, 34A12, 31B10
Submitted from: talponen at iki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.0528
or
http://arXiv.org/abs/1402.0528
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Trond A. Abrahamsen, Johann Langemets, and Vegard Lima
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 5 Feb 2014 14:31:28 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Almost square Banach spaces"
by Trond A. Abrahamsen, Johann Langemets, and Vegard Lima.
Abstract: We single out and study a natural class of Banach spaces
-- almost square Banach spaces. These spaces have duals that are
octahedral and finite convex combinations of slices of the unit ball of
an almost square space have diameter 2. We provide several examples and
characterizations of almost square spaces. In an almost square space we
can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere,
a unit vector $y$ such that $\|x_i+y\|$ is almost one. We prove that
non-reflexive spaces which are M-ideals in their biduals are almost
square.
We show that every space containing a copy of $c_0$ can be renormed
to be almost square. A local and a weak version of almost square spaces
are also studied.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B04, 46B07
Remarks: 22 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/1402.0818
or
http://arXiv.org/abs/1402.0818
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Apostolos Giannopoulos and Emanuel Milman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:41:11 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$M$-estimates for isotropic convex
bodies and their $L_q$-centroid bodies" by Apostolos Giannopoulos and
Emanuel Milman.
Abstract: Let $K$ be a centrally-symmetric convex body in $\mathbb{R}^n$
and let $\|\cdot\|$ be its induced norm on ${\mathbb R}^n$. We show
that if $K \supseteq r B_2^n$ then: \[ \sqrt{n} M(K) \leqslant C
\sum_{k=1}^{n} \frac{1}{\sqrt{k}} \min\left(\frac{1}{r} , \frac{n}{k}
\log\Big(e + \frac{n}{k}\Big) \frac{1}{v_{k}^{-}(K)}\right) . \] where
$M(K)=\int_{S^{n-1}} \|x\|\, d\sigma(x)$ is the mean-norm, $C>0$ is a
universal constant, and $v^{-}_k(K)$ denotes the minimal volume-radius of
a $k$-dimensional orthogonal projection of $K$. We apply this result to
the study of the mean-norm of an isotropic convex body $K$ in ${\mathbb
R}^n$ and its $L_q$-centroid bodies. In particular, we show that if $K$
has isotropic constant $L_K$ then: \[
M(K) \leqslant \frac{C\log^{2/5}(e+ n)}{\sqrt[10]{n}L_K} . \]
Archive classification: math.FA
Remarks: 19 pages
Submitted from: emanuel.milman at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.0904
or
http://arXiv.org/abs/1402.0904
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Trond A. Abrahamsen, Johann Langemets,
Vegard Lima and Olav Nygaard
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:43:08 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Observations on thickness and
thinness of Banach spaces" by Trond A. Abrahamsen, Johann Langemets,
Vegard Lima and Olav Nygaard.
Abstract: The aim of this note is to complement and extend some recent
results on Whitley's indices of thinness and thickness. As an example
we prove that every Banach space $X$ containing a copy of $c_0$ can be
equivalently renormed so that we at the same time have that $c_0$ becomes
an M-ideal and both the thickness and thinness index of $X$ equal 1.
Archive classification: math.FA
Remarks: 8 pages
Submitted from: trond.a.abrahamsen at uia.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.0996
or
http://arXiv.org/abs/1402.0996
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Szymon Draga
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:44:42 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On weakly locally uniformly rotund
norms which are not locally rotund" by Szymon Draga.
Abstract: We show that every infinite-dimensional Banach space with
separable dual admits an equivalent norm which is weakly locally uniformly
rotund but not locally uniformly rotund.
Archive classification: math.FA
Submitted from: szymon.draga at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.1097
or
http://arXiv.org/abs/1402.1097
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Goulnara Arzhantseva and Romain Tessera
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:46:30 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Relatively expanding box spaces
with no expansion" by Goulnara Arzhantseva and Romain Tessera.
Abstract: We exhibit a finitely generated group $G$ and a sequence of
finite index normal subgroups $N_n\trianglelefteq G$ such that for every
finite generating subset $S\subseteq G$, the sequence of finite Cayley
graphs $(G/N_n, S)$ does not coarsely embed into any $L^p$-space for
$1\leqslant p<\infty$ (moreover, into any uniformly curved Banach space),
and yet admits no weakly embedded expander.
Archive classification: math.GR math.FA math.MG
Mathematics Subject Classification: 46B85, 20F69, 22D10, 20E22
Remarks: 20 pages
Submitted from: goulnara.arjantseva at univie.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.1481
or
http://arXiv.org/abs/1402.1481
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Duanxu Dai
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:47:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantifying (weak) injectivity
of a Banach space and its second dual" by Duanxu Dai.
Abstract: Let $X$, $Y$ be two Banach spaces. Let $\varepsilon\geq
0$. A mapping $f: X\rightarrow Y$ is said a standard $\varepsilon-$
isometry if $f(0)=0$ and $\|f(x)-f(y)\|-\|x-y\|\leq \eps$. In this
paper, we first show that if $X$ is a separable Banach space and $Y^*$
has the point of $w^*$-norm continuity property(in short,$w^*$-PCP),
then for every standard $\varepsilon-$ isometry $f:X\rightarrow Y$
there exists a $w^*$-dense $G_\delta$ subset $\Omega$ of $ExtB_{X^*}$
such that there is a bounded linear operator $T: Y\rightarrow
C(\Omega,\tau_{w^*})$ with $\|T\|=1$ such that $Tf-Id$ is uniformly
bounded by $4\eps$ on $X$. More general results are also given. As a
corollary, we obtain quantitative characterizations of injectivity,
cardinality injectivity and separably injectivity of a Banach space
and its second dual which turn out to give a positive answer to Qian's
problem of 1995 in the sense of universality. We also discuss Qian's
problem in a $\mathcal{L}_{\infty,\lambda}$-space, $C(K)$-space for
a compact Hausdorff space $K$. Moreover, by using some results from
Avil$\acute{e}$s-S$\acute{a}$nchez-Castillo-Gonz$\acute{a}$lez- Moreno,
Cheng-Dong-Zhang, Johnson-Oikhberg, Rosenthal and Lindenstrauss, estimates
for several separably injective Banach spaces are given. Finally, we
show a more sharp quantitative and generalized Sobczyk 's theorem.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, 46B20, 47A58, Secondary
26E25, 54C60, 54C65, 46A20
Remarks: 21 page
Submitted from: dduanxu at 163.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.2123
or
http://arXiv.org/abs/1402.2123
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Brudnyi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:49:35 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On near-optimal admissible meshes"
by Alexander Brudnyi.
Abstract: We show that every compact subset of $\mathbb C^n$ admits a
near-optimal admissible mesh. We apply this result to study geometric
properties of Banach spaces of traces of real polynomials on $\mathbb R^n$
to compact subsets equipped with supremum norms.
Archive classification: math.FA
Mathematics Subject Classification: 41A10, 41A17, 65D05
Remarks: 6 pages
Submitted from: albru at math.ucalgary.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.2303
or
http://arXiv.org/abs/1402.2303
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Quanhua Xu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:51:14 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$H^\infty$ functional calculus
and maximal inequalities for semigroups of contractions on vector-valued
$L_p$-spaces" by Quanhua Xu.
Abstract: Let $\{T_t\}_{t>0}$ be a strongly continuous semigroup of
positive contractions on $L_p(X,\mu)$ with $1<p<\infty$. Let $E$ be
a UMD Banach lattice of measurable functions on another measure space
$(\Omega,\nu)$. For $f\in L_p(X; E)$ define
$$\mathcal M(f)(x,
\omega)=\sup_{t>0}\frac1t\Big|\int_0^tT_s(f(\cdot,\omega))(x)ds\Big|,\quad
(x,\omega)\in X\times\Omega.$$ Then the following maximal ergodic
inequality holds
$$\big\|\mathcal M(f)\big\|_{L_p(X; E)}\lesssim \big\|f\big\|_{L_p(X;
E)},\quad f\in L_p(X; E).$$ If the semigroup $\{T_t\}_{t>0}$ is
additionally assumed to be analytic, then $\{T_t\}_{t>0}$ extends to
an analytic semigroup on $L_p(X; E)$ and $\mathcal M(f)$ in the above
inequality can be replaced by the following sectorial maximal function
$$\mathcal T_\theta(f)(x, \omega)=\sup_{|{\rm
arg}(z)|<\theta}\big|T_z(f(\cdot,\omega))(x)\big|$$ for some $\theta>0$.
Under the latter analyticity assumption and if $E$ is a complex
interpolation
space between a Hilbert space and a UMD Banach space, then $\{T_t\}_{t>0}$
extends to an analytic semigroup on $L_p(X; E)$ and its negative generator
has a bounded $H^\infty(\Sigma_\sigma)$ calculus for some $\sigma<\pi/2$.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 47A35, 47A60. Secondary:
46B20, 42B25
Submitted from: quanhua.xu at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.2344
or
http://arXiv.org/abs/1402.2344
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joanna Garbulinska - Wegrzyn
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:52:59 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An isometrically universal Banach
space with a monotone Schauder" by Joanna Garbulinska - Wegrzyn.
Abstract: We present an isometric version of the complementably universal
Banach space $\mathcal{B}$ with a monotone Schauder basis. The space
$\mathcal{B}$ 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
Remarks: 10 pages
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/1402.2660
or
http://arXiv.org/abs/1402.2660
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel J. Fresen and Richard A. Vitale
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:54:25 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Concentration of random polytopes
around the expected convex hull" by Daniel J. Fresen and Richard
A. Vitale.
Abstract: We provide a streamlined proof and improved estimates for
the weak multivariate Gnedenko law of large numbers on concentration
of random polytopes within the space of convex bodies (in a fixed or
a high dimensional setting), as well as a corresponding strong law of
large numbers.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60D05, 60F99, 52A20, 52A22, 52B11
Remarks: 8 pages
Submitted from: daniel.fresen at yale.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.2718
or
http://arXiv.org/abs/1402.2718
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikko Kemppainen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:55:58 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On vector-valued tent spaces
and Hardy spaces associated with non-negative self-adjoint operators"
by Mikko Kemppainen.
Abstract: In this paper we study Hardy spaces associated with non-negative
self-adjoint operators and develop their vector-valued theory. The
complex interpolation scales of vector-valued tent spaces and Hardy
spaces are extended to the endpoint p=1. The holomorphic functional
calculus of L is also shown to be bounded on the associated Hardy space
H^1_L(X). These results, along with the atomic decomposition for the
aforementioned space, rely on boundedness of certain integral operators
on the tent space T^1(X).
Archive classification: math.FA
Mathematics Subject Classification: 42B35 (Primary), 46E40 (Secondary)
Remarks: 19 pages
Submitted from: mikko.k.kemppainen at helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.2886
or
http://arXiv.org/abs/1402.2886
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by U. Caglar, M. Fradelizi, O. Guedon, J.
Lehec, C. Schuett and E. M. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 21 Feb 2014 13:59:47 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Functional versions of L_p-affine
surface area and entropy" by U. Caglar, M. Fradelizi, O. Guedon, J. Lehec,
C. Schuett and E. M. Werner.
Abstract: In contemporary convex geometry, the rapidly developing
L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn
Minkowski theory. A cornerstone of this theory is the L_p-affine surface
area for convex bodies. Here, we introduce a functional form of this
concept, for log concave and s-concave functions. We show that the new
functional form is a generalization of the original L_p-affine surface
area. We prove duality relations and affine isoperimetric inequalities
for log concave and s-concave functions. This leads to a new inverse
log-Sobolev inequality for s-concave densities.
Archive classification: math.FA
Submitted from: elisabeth.werner at case.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.3250
or
http://arXiv.org/abs/1402.3250
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Second Announcement - BWB 2014
From: valentin ferenczi <ferenczi.math at gmail.com>
Date: Tue, 25 Feb 2014 11:00:35 -0300 (08:00 CST)
To: banach at math.okstate.edu
2nd ANNOUNCEMENT OF BWB 2014
First Brazilian Workshop in Geometry of Banach Spaces
August 25-29, 2014
Maresias, São Paulo State, Brazil.
This is the 2nd announcement for the First Brazilian Workshop in
Geometry of Banach Spaces, organized by the University of São Paulo
(USP), in the week August 25-29, 2014.
This international conference will take place at the Beach Hotel
Maresias, on the coast of São Paulo State, in Maresias. The scientific
program will focus on the theory of geometry of Banach spaces, with
emphasis on the following directions: linear theory of infinite
dimensional spaces and its relations to Ramsey theory, homological
theory and set theory; nonlinear theory; and operator theory.
Registration and abstract submissions are now open on the website
of conference:
http://www.ime.usp.br/~banach/bwb2014/
Deadline for registration is June 30th and for abstract submission
is April 30th. Please consult the website for all information and
contact us at bwb2014 at gmail.com if you have any question.
Plenary speakers:
S. A. Argyros (Nat. Tech. U. Athens)
J. M. F. Castillo (U. Extremadura)
P. Dodos (U. Athens)
G. Godefroy (Paris 6)
R. Haydon (U. Oxford)
W. B. Johnson (Texas A&M)
P. Koszmider (Polish Acad. Warsaw)
G. Pisier (Paris 6 & Texas A&M)
C. Rosendal (U. Illinois Chicago)
G. Schechtman (Weizmann Inst.)
Th. Schlumprecht (Texas A&M)
S. Todorcevic (Paris 7 & U. Toronto)
Scientific committee
J. M. F. Castillo (U. Extremadura)
V. Ferenczi (U. São Paulo, chair)
R. Haydon (U. Oxford)
W. B. Johnson (Texas A&M)
G. Pisier (Paris 6 & Texas A&M)
Th. Schlumprecht (Texas A&M)
S. Todorcevic (Paris 7 & U. Toronto)
The organizers,
F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad.
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Integration,
Vector Measures and Related Topics VI - a reminder
From: Grzegorz Plebanek <Grzegorz.Plebanek at math.uni.wroc.pl>
Date: Tue, 25 Feb 2014 19:24:46 +0100 (CET)
To: banach at math.okstate.edu
This is a reminder about the conference
THE MEETING: Integration, Vector Measures and Related Topics VI
WHEN: June 15 - 21, 2014
WHERE: the Mathematical Research and Conference Center in Bedlewo (near
Poznan, Poland),
REGISTRATION and more information on the conference webpage:
http://www.math.uni.wroc.pl/~drygier/ivmrt2014/
INVITED SPEAKERS: Antonio Aviles (Murcia), Erik J. Balder (Utrecht),
Oscar Blasco (Valencia), Guillermo Curbera (Sevilla), Luisa Di Piazza
(Palermo), Harold Garth Dales (Lancaster)
Joe Diestel (Kent), Marian Fabian (Prague), David H. Fremlin (Colchester),
Ondrej Kalenda (Prague), Zbigniew Lipecki
(Wrocaw), Jose Rodriguez (Murcia)
The organizing committee: M. Balcerzak, M. Cichon, K. Musial, G. Plebanek
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
From: Dale Alspach <alspach at math.okstate.edu>
Subject: [Banach] Piotr Mankiewicz
Date: Wed, 26 Feb 2014 19:00:22 -0600
With a deep regret we have to inform that Piotr Mankiewicz
suddenly passed away on February 21, 2014. We lost a good
friend and a good mathematician. He will be missed.
If you would like to send a few words to his family
please send it to his daughter Ania, at
annamankiewicz at gmail.com
Nicole Tomczak-Jaegermann
_______________________________________________
Banach mailing list
Banach at www.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 Vladimir P. Fonf and Clemente Zanco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 10 Mar 2014 14:49:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Almost overcomplete and almost
overtotal sequences in Banach spaces" by Vladimir P. Fonf and Clemente
Zanco.
Abstract: The new concepts are introduced of almost overcomplete
sequence in a Banach space and almost overtotal sequence in a dual
space. We prove that any of such sequences is relatively norm-compact
and we obtain several applications of this fact.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B50, 46B45
Submitted from: clemente.zanco at unimi.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.6247
or
http://arXiv.org/abs/1402.6247
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Despoina Zisimopoulou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 10 Mar 2014 14:52:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bourgain-Delbaen
$\mathcal{L}^{\infty}$-sums of Banach spaces" by Despoina Zisimopoulou.
Abstract: Motivated by a problem stated by S.A.Argyros and
Th. Raikoftsalis, we introduce a new class of Banach spaces. Namely, for a
sequence of separable Banach spaces $(X_n,\|\cdot\|_n)_{n\in\mathbb{N}}$,
we define the Bourgain Delbaen $\mathcal{L}^{\infty}$-sum of the sequence
$(X_n,\|\cdot\|_n)_{n\in\mathbb{N}}$ which is a Banach space $\mathcal{Z}$
constructed with the Bourgain-Delbaen method. In particular, for every
$1\leq p<\infty$, taking $X_n=\ell_p$ for every $n\in\mathbb{N}$ the
aforementioned space $\mathcal{Z}_p$ is strictly quasi prime and admits
$\ell_p$ as a complemented subspace. We study the operators acting on
$\mathcal{Z}_p$ and we prove that for every $n\in\mathbb{N}$, the space
$\mathcal{Z}^n_p=\sum_{i=1}^n\oplus \mathcal{Z}_p$ admits exactly $n+1$,
pairwise not isomorphic, complemented subspaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B25, 46B28
Remarks: 29 pages, no figures
Submitted from: dzisimopoulou at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1402.6564
or
http://arXiv.org/abs/1402.6564
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Elbour, N. Machrafi, and M. Moussa
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 10 Mar 2014 14:53:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the class of weak almost
limited operators" by A. Elbour, N. Machrafi, and M. Moussa.
Abstract: We introduce and study the class of weak almost limited
operators. We establish a characterization of pairs of Banach lattices
$E$, $F$ for which every positive weak almost limited operator
$T:E\rightarrow F$ is almost limited (resp. almost Dunford-Pettis). As
consequences, we will give some interesting results.
Archive classification: math.FA
Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65
(Secondary)
Submitted from: azizelbour at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.0136
or
http://arXiv.org/abs/1403.0136
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, 10 Mar 2014 14:55:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the $c_0$-extension property
for compact lines" by Claudia Correa and Daniel V. Tausk.
Abstract: We present a characterization of the continuous increasing
surjections $\phi:K\to L$ between compact lines $K$ and $L$ for which
the corresponding subalgebra $\phi^*C(L)$ has the $c_0$-extension
property in $C(K)$. A natural question arising in connection with this
characterization is shown to be independent of the axioms of ZFC.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46E15, 54F05
Remarks: 12 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/1403.0605
or
http://arXiv.org/abs/1403.0605
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, 10 Mar 2014 14:56:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A proof of Rosenthal's \(\ell_1\)
Theorem" by Ioannis Gasparis.
Abstract: A proof is given of Rosenthal's \(\ell_1\) theorem.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Remarks: 5 pages
Submitted from: ioagaspa at math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.1163
or
http://arXiv.org/abs/1403.1163
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Kaminska, Karol Lesnik, and Yves
Raynaud
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 10 Mar 2014 14:58:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Dual spaces to Orlicz - Lorentz
spaces" by Anna Kaminska, Karol Lesnik, and Yves Raynaud.
Abstract: For an Orlicz function $\varphi$ and a decreasing weight $w$,
two intrinsic exact descriptions are presented for the norm in the
K\"othe dual of an Orlicz-Lorentz function space $\Lambda_{\varphi,w}$
or a sequence space $\lambda_{\varphi,w}$, equipped with either
Luxemburg or Amemiya norms. The first description of the dual norm is
given via the modular $\inf\{\int\varphi_*(f^*/|g|)|g|: g\prec w\}$,
where $f^*$ is the decreasing rearrangement of $f$, $g\prec w$ denotes
the submajorization of $g$ by $w$ and $\varphi_*$ is the complementary
function to $\varphi$. The second one is stated in terms of the modular
$\int_I \varphi_*((f^*)^0/w)w$, where $(f^*)^0$ is Halperin's level
function of $f^*$ with respect to $w$. That these two descriptions
are equivalent results from the identity $\inf\{\int\psi(f^*/|g|)|g|:
g\prec w\}=\int_I \psi((f^*)^0/w)w$ valid for any measurable function $f$
and Orlicz function $\psi$. Analogous identity and dual representations
are also presented for sequence spaces.
Archive classification: math.FA
Mathematics Subject Classification: 42B25, 46B10, 46E30
Remarks: 25 pages
Submitted from: klesnik at vp.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.1505
or
http://arXiv.org/abs/1403.1505
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Deping Ye
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 10 Mar 2014 15:00:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New Orlicz affine isoperimetric
inequalities" by Deping Ye.
Abstract: The Orlicz-Brunn-Minkowski theory receives considerable
attention recently, and many results in the $L_p$-Brunn-Minkowski theory
have been extended to their Orlicz counterparts. The aim of this paper
is to develop Orlicz $L_{\phi}$ affine and geominimal surface areas
for single convex body as well as for multiple convex bodies, which
generalize the $L_p$ (mixed) affine and geominimal surface areas --
fundamental concepts in the $L_p$-Brunn-Minkowski theory. Our extensions
are different from the general affine surface areas by Ludwig (in
Adv. Math. 224 (2010)). Moreover, our definitions for Orlicz $L_{\phi}$
affine and geominimal surface areas reveal that these affine invariants
are essentially the infimum/supremum of $V_{\phi}(K, L^\circ)$, the Orlicz
$\phi$-mixed volume of $K$ and the polar body of $L$, where $L$ runs over
all star bodies and all convex bodies, respectively, with volume of $L$
equal to the volume of the unit Euclidean ball $B_2^n$. Properties for
the Orlicz $L_{\phi}$ affine and geominimal surface areas, such as,
affine invariance and monotonicity, are proved. Related Orlicz affine
isoperimetric inequalities are also established.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 53A15
Submitted from: deping.ye at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.1643
or
http://arXiv.org/abs/1403.1643
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 13:53:26 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by B. Bongiorno, U. B. Darju, and L. Di Piazza
This is an announcement for the paper "Lineability of non-differentiable
Pettis primitives" by B. Bongiorno, U. B. Darju, and L. Di Piazza.
Abstract: Let X be an in?nite-dimensional Banach space. In 1995, settling
a long outstanding problem of Pettis, Dilworth and Girardi constructed an
X-valued Pettis integrable function on [0; 1] whose primitive is nowhere
weakly di?erentiable. Using their technique and some new ideas we show
that ND, the set of strongly measurable Pettis integrable functions with
nowhere weakly di?erentiable primitives, is lineable, i.e., there is an
in?nite dimensional vector space whose nonzero vectors belong to ND.
Archive classification: math.FA
Mathematics Subject Classification: 46G10, 28B05
Submitted from: ubdarj01 at louisville.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.1908
or
http://arXiv.org/abs/1403.1908
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 13:55:47 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Sheng Zhang
This is an announcement for the paper "Coarse quotient mappings between
metric spaces" by Sheng Zhang.
Abstract: We give a definition of coarse quotient mapping and show
that several results for uniform quotient mapping also hold in the
coarse setting. In particular, we prove that any Banach space that is
a coarse quotient of $L_p\equiv L_p[0,1]$, $1<p<\infty$, is isomorphic
to a linear quotient of $L_p$. It is also proved that $\ell_q$ is not a
coarse quotient of $\ell_p$ for $1<p<q<\infty$ using Rolewicz's property
($\beta$).
Archive classification: math.FA math.MG
Submitted from: z1986s at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.1934
or
http://arXiv.org/abs/1403.1934
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 13:58:14 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Jan-David Hardtke
This is an announcement for the paper "WORTH property, Garc\'{i}a-Falset
coefficient and Opial property of infinite sums" by Jan-David Hardtke.
Abstract: We prove some results concerning the WORTH property and
the Garc\'{i}a-Falset coefficient of absolute sums of infinitely many
Banach spaces. The Opial property/uniform Opial property of infinite
$\ell^p$-sums is also studied and some properties analogous to the Opial
property/uniform Opial property for Lebesgue-Bochner spaces $L^p(\mu,X)$
are discussed.
Archive classification: math.FA
Mathematics Subject Classification: 46B20 46E40
Remarks: 22 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/1403.2647
or
http://arXiv.org/abs/1403.2647
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:00:20 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by A. Elbour, N. Machrafi, and M. Moussa
This is an announcement for the paper "Weak compactness of almost limited
operators" by A. Elbour, N. Machrafi, and M. Moussa.
Abstract: The paper is devoted to the relationship between almost limited
operators and weakly compacts operators. We show that if $F$ is a $\sigma
$-Dedekind complete Banach lattice then, every almost limited operator
$T:E\rightarrow F $ is weakly compact if and only if $E$ is reflexive
or the norm of $F$ is order continuous. Also, we show that if $E$ is
a $\sigma $-Dedekind complete Banach lattice then the square of every
positive almost limited operator $ T:E\rightarrow E$ is weakly compact
if and only if the norm of $E$ is order continuous.
Archive classification: math.FA
Mathematics Subject Classification: 46B42 (Primary) 46B50, 47B65
(Secondary)
Remarks: 5 pages
Submitted from: azizelbour at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.3348
or
http://arXiv.org/abs/1403.3348
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:02:59 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Dustin G. Mixon
This is an announcement for the paper "Explicit matrices with the
Restricted Isometry Property: Breaking the square-root bottleneck"
by Dustin G. Mixon.
Abstract: Matrices with the restricted isometry property (RIP) are
of particular interest in compressed sensing. To date, the best
known RIP matrices are constructed using random processes, while
explicit constructions are notorious for performing at the "square-root
bottleneck," i.e., they only accept sparsity levels on the order of the
square root of the number of measurements. The only known explicit matrix
which surpasses this bottleneck was constructed by Bourgain, Dilworth,
Ford, Konyagin and Kutzarova. This chapter provides three contributions
to further the groundbreaking work of Bourgain et al.: (i) we develop an
intuition for their matrix construction and underlying proof techniques;
(ii) we prove a generalized version of their main result; and (iii)
we apply this more general result to maximize the extent to which their
matrix construction surpasses the square-root bottleneck.
Archive classification: math.FA cs.IT math.CO math.IT
Remarks: Book chapter, submitted to Compressed Sensing and its
Applications
Submitted from: dustin.mixon at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.3427
or
http://arXiv.org/abs/1403.3427
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:05:20 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Ralf Beckmann and Anton Deitmar
This is an announcement for the paper "Two application of nets" by Ralf
Beckmann and Anton Deitmar.
Abstract: Two applications of nets are given. The first is an extension
of the Bochner integral to arbitrary locally convex spaces, leading to an
integration theorye of more general vector valued functions then in the
classical approach by Gelfand and Pettis. The second application starts
with the observation that an operator on a Hilbert space is trace class if
and only if the net of ``principal trace minors'' converges. The notion
of a ``determinant class operator'' then is defined as one for which the
net of determinantal principal minors converges. It is shown that for
a normal operator A this condition coincides with 1-A being trace class.
Archive classification: math.FA
Submitted from: deitmar at uni-tuebingen.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.3207
or
http://arXiv.org/abs/1403.3207
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:08:02 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by S. J. Dilworth, D. Kutzarova, E. Odell, Th.
Sch
***lumprecht and A. Zsak
This is an announcement for the paper "Renorming spaces with greedy bases"
by S. J. Dilworth, D. Kutzarova, E. Odell, Th. Schlumprecht and A. Zsak.
Abstract: We study the problem of improving the greedy constant or the
democracy constant of a basis of a Banach space by renorming. We prove
that every Banach space with a greedy basis can be renormed, for a
given $\vare>0$, so that the basis becomes $(1+\vare)$-democratic, and
hence $(2+\vare)$-greedy, with respect to the new norm. If in addition
the basis is bidemocratic, then there is a renorming so that in the new
norm the basis is $(1+\vare)$-greedy. We also prove that in the latter
result the additional assumption of the basis being bidemocratic can
be removed for a large class of bases. Applications include the Haar
systems in $L_p[0,1]$, $1<p<\infty$, and in dyadic Hardy space $H_1$,
as well as the unit vector basis of Tsirelson space.
Archive classification: math.FA
Mathematics Subject Classification: 41A65, 41A44, 41A50, 46B03
Submitted from: schlump at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.3777
or
http://arXiv.org/abs/1403.3777
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:10:10 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by F. Baudier, D. Freeman, Th. Schlumprecht
and A.
*** Zsak
This is an announcement for the paper "The metric geometry of the Hamming
cube and applications" by F. Baudier, D. Freeman, Th. Schlumprecht and
A. Zsak.
Abstract: The Lipschitz geometry of segments of the infinite Hamming
cube is studied. Tight estimates on the distortion necessary to
embed the segments into spaces of continuous functions on countable
compact metric spaces are given. As an application, the first nontrivial
lower bounds on the $C(K)$-distortion of important classes of separable
Banach spaces, where $K$ is a countable compact space in the family $ \{
[0,\omega],[0,\omega\cdot 2],\dots, [0,\omega^2], \dots, [0,\omega^k\cdot
n],\dots,[0,\omega^\omega]\}\ ,$ are obtained.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B85
Submitted from: schlump at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.4376
or
http://arXiv.org/abs/1403.4376
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:12:28 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Marek Cuth and Ondrej F.K. Kalenda
This is an announcement for the paper "Monotone retractability and
retractional skeletons" by Marek Cuth and Ondrej F.K. Kalenda.
Abstract: We prove that a countably compact space is monotonically
retractable if and only if it has a full retractional skeleton. In
particular, a compact space is monotonically retractable if and only if it
is Corson. This gives an answer to a question of R. Rojas-Hern{\'a}ndez
and V. V. Tkachuk. Further, we apply this result to characterize
retractional skeleton using a topology on the space of continuous
functions, answering thus a question of the first author and a related
question of W. Kubi\'s.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 54C15, 54D30, 46B26
Remarks: 14 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/1403.4480
or
http://arXiv.org/abs/1403.4480
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:15:10 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Daniel Carando, Veronica Dimant, Pablo
Sevilla-
***Peris and Roman Villafane
This is an announcement for the paper "Diagonal extendible multilinear
operators between $\ell_p$-spaces" by Daniel Carando, Veronica Dimant,
Pablo Sevilla-Peris and Roman Villafane.
Abstract: We study extendibility of diagonal multilinear operators from
$\ell_p$ to $\ell_q$ spaces. We determine the values of $p$ and $q$
for which every diagonal $n$-linear operator is extendible, and those
for which the only extendible ones are integral. We address the same
question for multilinear forms on $\ell_p$.
Archive classification: math.FA
Mathematics Subject Classification: 47H60, 46B45, 46G25
Submitted from: rvillafa at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.4577
or
http://arXiv.org/abs/1403.4577
Return-path: <alspach at math.okstate.edu>
Date: Sun, 30 Mar 2014 14:20:09 CDT
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by C. Angosto, M. C. Listan-Garcia, and F.
Rambla-
***Barreno
This is an announcement for the paper "Continuity properties of
sequentially asymptotically center-complete spaces" by C. Angosto,
M. C. Listan-Garcia, and F. Rambla-Barreno.
Abstract: We obtain formulae to calculate the asymptotic center and
radius of bounded sequences in ${\cal C}_0(L)$ spaces. We also study
the existence of continuous selectors for the asymptotic center map in
general Banach spaces. In Hilbert spaces, even a H\"older-type estimation
is given.
Archive classification: math.FA
Mathematics Subject Classification: 41A50 (Primary) 46E15 (Secondary)
Submitted from: fernando.rambla at uca.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.4646
or
http://arXiv.org/abs/1403.4646
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Geometry of Banach Spaces - A conference in honor of
Stanimir Troyanski
From: Jose Rodriguez <joserr at um.es>
Date: Wed, 02 Apr 2014 08:53:24 +0200
To: banach at math.okstate.edu
Dear colleagues:
This is the third announcement of the conference
Geometry of Banach Spaces - A conference in honor of Stanimir Troyanski
which will be held in Albacete (Spain) on June 10-13, 2014, on the
occasion of the 70th birthday of Stanimir Troyanski.
The deadline for early registration is April 30.
Our web page at
https://sites.google.com/site/geometryofbanachspaces/
contains detailed information about the conference, including:
registration and payment, abstract submission, accommodation and travel.
Main speakers who accepted our invitation are: S. Argyros, J. Castillo,
S. Dilworth, M. Fabian, V. Fonf, P. Hajek, R. Haydon, F. Hernandez, P.
Kenderov, P. Koszmider, D. Kutzarova, V. Milman, A. Molto, J. Revalski,
T. Schlumprecht, R. Smith, A. Suarez Granero.
In addition, participants will have the opportunity to deliver a short
talk.
Please do not hesitate in contacting us at
geometry.banach.spaces.2014 at gmail.com if you need further information.
Looking forward to meeting you!
The organizers,
A. Aviles, S. Lajara, J.P. Moreno, J. Rodriguez.
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Workshop at Texas A&M
From: Bill Johnson <johnson at math.tamu.edu>
Date: Thu, 10 Apr 2014 13:56:33 -0500 (CDT)
To: banach at math.okstate.edu
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2014
The Summer 2014 Workshop in Analysis and Probability at Texas A&M
University will be in session from July 1 to 31, 2014. All activities will
take
place in the Blocker Building. The homepage of the Workshop can be
found at
http://www.math.tamu.edu/~kerr/workshop
The Summer Informal Regional Functional Analysis Seminar (SUMIRFAS)
will be held July 25-27.
July 21-25 there will be a Concentration Week on "Free Probability",
organized by Michael Anshelevich, Ken Dykema, and John Williams.
This meeting aims both to introduce younger researchers to this
fast-growing field and to showcase the latest results. Topics discussed
will include operator algebras, connections to random matrix theory,
operator-valued and fully matricial techniques, stochastic processes,
limit theorems, and free stochastic differential equations. The program
will feature lecture series by Greg Anderson, Serban Belinschi, and
Dimitri Shlyakhtenko. The homepage can be found at
http://www.math.tamu.edu/~jwilliams/Free_Probability_2014
Also, June 9-13 there will be a Concentration Week on "Groups, Groupoids,
and Dynamics" organized by David Kerr and Volodymyr Nekrashevych
(note the special dates, which fall outside the scope of the main Workshop
period). This meeting aims to provide a forum for understanding and
exploring various recent developments in groups and dynamics that revolve
around groupoids and equivalence relations. Topics will include
topological
orbit equivalence, amenability, hyperbolicity, self-similar groups,
entropy,
and rigidity in measurable group theory. Lectures series will be given
by Lewis Bowen and Thierry Giordano. The homepage can be found at
http://www.math.tamu.edu/~kerr/concweek14
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 "Free Probability"
contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema
<ken.dykema at math.tamu.edu>, or John Williams <jwilliams at math.tamu.edu>
For information about the Concentration Week on "Groups, Groupoids,
Dynamics" contact David Kerr <kerr at math.tamu.edu> or Volodymyr
Nekrashevych <nekrash at math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at www.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 Oleg Reinov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:10:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some thoughts on approximation
properties" by Oleg Reinov.
Abstract: We study some known approximation properties and introduce and
investigate several new approximation properties, closely connected with
different quasi-normed tensor products. These are the properties like the
$AP_s$ or $AP_{(s,w)}$ for $s\in (0,1],$ which give us the possibility
to identify the spaces of $s$-nuclear and $(s,w)$-nuclear operators with
the corresponding tensor products (e.g., related to Lorentz sequence
spaces). Some applications are given (in particular, we present not
difficult proofs of the trace-formulas of Grothendieck-Lidskii type for
several ideals of nuclear operators).
Archive classification: math.FA
Mathematics Subject Classification: 46B28 Spaces of operators, tensor
products, approximation
Remarks: 17 pages. A talk at "July 22-26 Positivity 2013 Holland, Leiden"
Submitted from: orein51 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.4746
or
http://arXiv.org/abs/1403.4746
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gustavo Araujo and Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:12:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spaceability and optimal
estimates for summing multilinear operators" by Gustavo Araujo and
Daniel Pellegrino.
Abstract: We show that given a positive integer $m$, a real
number $p\in\left[ 2,\infty\right) $ and $1\leq s<p^{\ast}$ the
set of non--multiple $\left( r,s\right) $--summing $m$--linear
forms on $\ell_{p}\times\cdots\times\ell_{p}$ is spaceable
whenever $r<\frac{2ms}{s+2m-ms}$. This result is optimal since
for $r\geq\frac{2ms}{s+2m-ms}$ all $m$--linear forms on $\ell
_{p}\times\cdots\times\ell_{p}$ are multiple $\left( r,s\right)
$--summing. Among other results, we improve some results from \cite{laa}
and generalize a result related to cotype (from 2010) due to Botelho,
Michels and the second named author. We also prove some new coincidence
results for the class of absolutely summing multilinear operators.
Archive classification: math.FA
Submitted from: pellegrino at pq.cnpq.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.6064
or
http://arXiv.org/abs/1403.6064
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando and Martin Mazzitelli
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:13:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bounded holomorphic functions
attaining their norms in the bidual" by Daniel Carando and Martin
Mazzitelli.
Abstract: Under certain hypotheses on the Banach space $X$, we prove
that the set of analytic functions in $\mathcal{A}_u(X)$ (the algebra
of all holomorphic and uniformly continuous functions in the ball
of $X$) whose Aron-Berner extensions attain their norms, is dense in
$\mathcal{A}_u(X)$. The result holds also for functions with values in a
dual space or in a Banach space with the so-called property $(\beta)$. For
this, we establish first a Lindenstrauss type theorem for continuous
polynomials. We also present some counterexamples for the Bishop-Phelps
theorem in the analytic and polynomial cases where our results apply.
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/1403.6431
or
http://arXiv.org/abs/1403.6431
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cedric Arhancet
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:15:24 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On a conjecture of Pisier on the
analyticity of semigroups" by Cedric Arhancet.
Abstract: We show that the analyticity of some semigroups $(T_t)_{t \geq
0}$ of contractive Fourier multipliers on $L^p$-spaces of compact abelian
groups is preserved by the tensorisation of the identity operator of
a Banach space for a large class of K-convex Banach spaces, answering
partially a conjecture of Pisier. We also give versions of this result
for some semigroups of Schur multipliers and Fourier multipliers on
noncommutative $L^p$-spaces. Finally, we give a precise description of
semigroups of Schur multipliers to which the result of this paper can
be applied.
Archive classification: math.FA
Remarks: 10 pages; comments are welcome
Submitted from: cedric.arhancet at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.6737
or
http://arXiv.org/abs/1403.6737
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pedro Levit Kaufmann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:16:46 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Products of Lipschitz-free spaces
and applications" by Pedro Levit Kaufmann.
Abstract: We show that, given a Banach space $X$, the Lipschitz-free
space over $X$, denoted by $\mathcal{F}(X)$, is isomorphic to
$(\sum_{n=1}^\infty \mathcal{F}(X))_{\ell_1}$. Some applications are
presented, including a non-linear version of Pe\l czy\'ski's decomposition
method for Lipschitz-free spaces and the identification up to isomorphism
between $\mathcal{F}(\mathbb{R}^n)$ and the Lipschitz-free space over
any compact metric space which is locally bi-Lipschitz embeddable into
$\mathbb{R}^n$ and which contains a subset that is Lipschitz equivalent
to the unit ball of $\mathbb{R}^n$. We also show that $\mathcal{F}(M)$
is isomorphic to $\mathcal{F}(c_0)$ for all separable metric spaces $M$
which are absolute Lipschitz retracts and contain a subset which is
Lipschitz equivalent to the unit ball of $c_0$. This class contains
all $C(K)$ spaces with $K$ infinite compact metric (Dutrieux and
Ferenczi had already proved that $\mathcal{F}(C(K))$ is isomorphic to
$\mathcal{F}(c_0)$ for those $K$ using a different method). Finally we
study Lipschitz-free spaces over certain unions and quotients of metric
spaces, extending a result by Godard.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46T99
Remarks: 17 pages, 1 figure
Submitted from: pkaufmann at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.6605
or
http://arXiv.org/abs/1403.6605
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mehdi Ghasemi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:18:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Integral representation of linear
functionals on function spaces" by Mehdi Ghasemi.
Abstract: Let $A$ be a vector space of real valued functions
on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear
functional. Given a $\sigma$-algebra $\mathcal{A}$, of subsets of $X$,
we present a necessary condition for $L$ to be representable as an
integral with respect to a measure $\mu$ on $X$ such that elements
of $\mathcal{A}$ are $\mu$-measurable. This general result then is
applied to the case where $X$ carries a topological structure and $A$
is a family of continuous functions and naturally $\mathcal{A}$ is the
Borel structure of $X$. As an application, short solutions for the
full and truncated $K$-moment problem are presented. An analogue of
Riesz-Markov-Kakutani representation theorem is given where $C_{c}(X)$
is replaced with whole $C(X)$. Then we consider the case where $A$
only consists of bounded functions and hence is equipped with $\sup$-norm.
Archive classification: math.FA
Mathematics Subject Classification: 47A57, 28C05, 28E99
Submitted from: mehdi.ghasemi at usask.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.6956
or
http://arXiv.org/abs/1403.6956
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Andreas Defant, and Pablo
Sevilla-Peris
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:19:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on a
Bohnenblust-Hille-Helson type inequality" by Daniel Carando, Andreas
Defant, and Pablo Sevilla-Peris.
Abstract: We give a variant of the Bohenblust-Hille inequality which,
for certain families of polynomials, leads to constants with polynomial
growth in the degree.
Archive classification: math.FA
Submitted from: psevilla at mat.upv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.7033
or
http://arXiv.org/abs/1403.7033
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Arnaud Marsiglietti
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:21:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On improvement of the concavity
of convex measures" by Arnaud Marsiglietti.
Abstract: We prove that a general class of measures, which includes
$\log$-concave measures, are $\frac{1}{n}$-concave in the terminology
of Borell under additional assumptions on the measure or on the sets,
such as symmetries. This generalizes results of Gardner and Zvavitch.
Archive classification: math.FA
Submitted from: arnaud.marsiglietti at univ-mlv.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1403.7643
or
http://arXiv.org/abs/1403.7643
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by O. Blasco, G. Botelho, D, Pellegrino, and
P. Rueda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:22:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Absolutely summing multilinear
operators on $\ell_p$ spaces" by O. Blasco, G. Botelho, D, Pellegrino,
and P. Rueda.
Abstract: We prove new summability properties for multilinear operators on
$\ell_p$ spaces. An important tool for this task is a better understanding
of the interplay between almost summing and absolutely summing multilinear
operators.
Archive classification: math.FA
Submitted from: pellegrino at pq.cnpq.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.1322
or
http://arXiv.org/abs/1404.1322
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Cwikel, Mario Milman and Richard
Rochberg
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:24:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An introduction to Nigel Kalton's
work on differentials of complex interpolation processes for Kothe spaces"
by Michael Cwikel, Mario Milman and Richard Rochberg.
Abstract: This paper contains no new results. It is intended to be merely
a brief introduction to the long paper:
N. J. Kalton, Differentials of complex interpolation processes
for Kothe
function spaces. Trans. Amer. Math. Soc. 333 (1992), no. 2, 479--529.
and to mention some possible directions for applying the powerful
methods
developed in Kalton's paper for further future research. The reader
should also be aware of other perspectives in other commentaries on
Kalton's paper, which appear in other sources to which we refer.
Archive classification: math.FA
Mathematics Subject Classification: 46B70 (Primary), 42B20, 42B30, 42B35,
46B42 (Secondary)
Remarks: 12 pages
Submitted from: mcwikel at math.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.2893
or
http://arXiv.org/abs/1404.2893
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jan van Neerven, Mark Veraar, and Lutz Weis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:30:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the R-boundedness of stochastic
convolution operators" by Jan van Neerven, Mark Veraar, and Lutz Weis.
Abstract: The $R$-boundedness of certain families of vector-valued
stochastic convolution operators with scalar-valued square integrable
kernels is the key ingredient in the recent proof of stochastic maximal
$L^p$-regularity, $2<p<\infty$, for certain classes of sectorial operators
acting on spaces $X=L^q(\mu)$, $2\le q<\infty$. This paper presents a
systematic study of $R$-boundedness of such families. Our main result
generalises the afore-mentioned $R$-boundedness result to a larger class
of Banach lattices $X$ and relates it to the $\ell^{1}$-boundedness
of an associated class of deterministic convolution operators. We also
establish an intimate relationship between the $\ell^{1}$-boundedness
of these operators and the boundedness of the $X$-valued maximal
function. This analysis leads, quite surprisingly, to an example showing
that $R$-boundedness of stochastic convolution operators fails in certain
UMD Banach lattices with type $2$.
Archive classification: math.FA math.PR
Mathematics Subject Classification: Primary: 60H15, Secondary: 42B25,
46B09, 46E30, 60H05
Submitted from: m.c.veraar at tudelft.nl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.3353
or
http://arXiv.org/abs/1404.3353
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Aude Dalet
From: alspach at math.okstate.edu (Dale Alspach)
Date: Wed, 16 Apr 2014 14:31:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Free spaces over some proper
metric spaces" by Aude Dalet.
Abstract: We prove that the Lipschitz-free space over a countable proper
metric space and over a proper ultrametric space is isometric to a dual
space and has the metric approximation property.
Archive classification: math.FA
Mathematics Subject Classification: 46B10, 46B28
Submitted from: aude.dalet at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.3939
or
http://arXiv.org/abs/1404.3939
ubject: Abstract of a paper by Rui F. Vigelis and Charles C. Cavalcante
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:30:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Smoothness of the Orlicz Norm
in Musielak-Orlicz Function Spaces" by Rui F. Vigelis and Charles
C. Cavalcante.
Abstract: In this paper, we present a characterization of support
functionals and smooth points in $L_{0}^{\Phi}$, the Musielak-Orlicz
space equipped with the Orlicz norm. As a result, criterion for the
smoothness of $L_{0}^{\Phi}$ is also obtained. Some expressions involving
the norms of functionals in $(L_{0}^{\Phi})^{*}$, the topological dual
of $L_{0}^{\Phi}$, are proved for arbitrary Musielak-Orlicz functions.
Archive classification: math.FA
Submitted from: rfvigelis at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.4306
or
http://arXiv.org/abs/1404.4306
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by N. Albuquerque, D. Nunez-Alarcon, J. Santos
and D. M. Serrano-Rodriguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:34:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Absolutely summing multilinear
operators via interpolation" by N. Albuquerque, D. Nunez-Alarcon,
J. Santos and D. M. Serrano-Rodriguez.
Abstract: We use an interpolative technique from \cite{abps} to introduce
the notion of multiple $N$-separately summing operators. Our approach
extends and unifies some recent results; for instance we recover the
best known estimates of the multilinear Bohnenblust-Hille constants
due to F. Bayart, D. Pellegrino and J. Seoane-Sep\'ulveda. More
precisely, as a consequence of our main result, for $1\leq t<2$
and $m\in \mathbb{N}$ we prove that $$ \left( \sum_{i_{1},\dots
,i_{m}=1}^{\infty }\left\vert U\left(e_{i_{1}},\dots ,e_{i_{m}}\right)
\right\vert^{\frac{2tm}{2+(m-1)t}}\right)^{\frac{2+(m-1)t}{2tm}}
\leq \left[\prod_{j=2}^{m}\Gamma \left( 2-\frac{2-t}{jt-2t+2}\right)
^{\frac{t(j-2)+2}{2t-2jt}}\right] \left\Vert U\right\Vert $$ for
all complex $m$-linear forms $U:c_{0}\times \cdot \cdot \cdot \times
c_{0}\rightarrow \mathbb{C}$.
Archive classification: math.FA
Submitted from: ngalbqrq at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.4949
or
http://arXiv.org/abs/1404.4949
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grigoris Paouris and Petros Valettas
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:36:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Neighborhoods on the Grasmannian
of marginals with bounded isotropic constant" by Grigoris Paouris and
Petros Valettas.
Abstract: We show that for any isotropic log-concave probability measure
$\mu$ on $\mathbb R^n$, for every $\varepsilon > 0$, every $1 \leq k
\leq \sqrt{n}$ and any $E \in G_{n,k}$ there exists $F \in G_{n,k}$
with $d(E,F) < \varepsilon$ and $L_{\pi_F\mu} < C/\varepsilon$.
Archive classification: math.FA
Submitted from: petvalet at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.4988
or
http://arXiv.org/abs/1404.4988
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez, Markus
Passenbrunner and Joscha Prochno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:38:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Probabilistic estimates for
tensor products of random vectors" by David Alonso-Gutierrez, Markus
Passenbrunner and Joscha Prochno.
Abstract: We prove some probabilistic estimates for tensor products
of random vectors. As an application we obtain embeddings of certain
matrix spaces into $L_1$.
Archive classification: math.FA
Mathematics Subject Classification: 46B09, 46B07, 46B28, 46B45
Remarks: 14 pages
Submitted from: joscha.prochno at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.5423
or
http://arXiv.org/abs/1404.5423
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Kamont and Markus Passenbrunner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:39:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Unconditionality of orthogonal
spline systems in $H^1$" by Anna Kamont and Markus Passenbrunner.
Abstract: We give a simple geometric characterization of knot sequences
for which the corresponding orthonormal spline system of arbitrary order
$k$ is an unconditional basis in the atomic Hardy space $H^1[0,1]$.
Archive classification: math.FA
Remarks: 31 pages
Submitted from: markus.passenbrunner at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.5493
or
http://arXiv.org/abs/1404.5493
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Luis Rademacher
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:41:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A simplicial polytope that
maximizes the isotropic constant must be a simplex" by Luis Rademacher.
Abstract: The isotropic constant $L_K$ is an affine-invariant measure of
the spread of a convex body $K$. For a $d$-dimensional convex body $K$,
$L_K$ can be defined by $L_K^{2d} = \det(A(K))/(\mathrm{vol}(K))^2$, where
$A(K)$ is the covariance matrix of the uniform distribution on $K$. It is
an outstanding open problem to find a tight asymptotic upper bound of the
isotropic constant as a function of the dimension. It has been conjectured
that there is a universal constant upper bound. The conjecture is known to
be true for several families of bodies, in particular, highly symmetric
bodies such as bodies having an unconditional basis. It is also known
that maximizers cannot be smooth.
In this work we study the gap between smooth bodies and highly symmetric
bodies by showing progress towards reducing to a highly symmetric case
among non-smooth bodies. More precisely, we study the set of maximizers
among simplicial polytopes and we show that if a simplicial $d$-polytope
$K$ is a maximizer of the isotropic constant among $d$-dimensional convex
bodies, then when $K$ is put in isotropic position it is symmetric around
any hyperplane spanned by a $(d-2)$-dimensional face and the origin. By
a result of Campi, Colesanti and Gronchi, this implies that a simplicial
polytope that maximizes the isotropic constant must be a simplex.
Archive classification: math.FA math.MG math.PR
Submitted from: lrademac at cse.ohio-state.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.5662
or
http://arXiv.org/abs/1404.5662
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Zakhar Kabluchko and Dmitry Zaporozhets
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:45:00 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Intrinsic volumes of Sobolev balls"
by Zakhar Kabluchko and Dmitry Zaporozhets.
Abstract: A formula due to Sudakov relates the first intrinsic volume
of a convex set in a Hilbert space to the maximum of the isonormal
Gaussian process over this set. Using this formula we compute the first
intrinsic volumes of infinite-dimensional convex compact sets including
unit balls with respect to Sobolev-type seminorms and ellipsoids in the
Hilbert space. We relate the distribution of the random one-dimensional
projections of these sets to the distributions $S_1,S_2,C_1,C_2$
studied by Biane, Pitman, Yor [Bull. AMS 38 (2001)]. We show that
the $k$-th intrinsic volume of the set of all functions on $[0,1]$
which have Lipschitz constant bounded by $1$ and which vanish at
$0$ (respectively, which have vanishing integral) is given by $$
V_k = \frac{\pi^{k/2}}{\Gamma\left(\frac 32 k +1 \right)}, \text{
respectively } V_k = \frac{\pi^{(k+1)/2}}{2\Gamma\left(\frac 32 k
+\frac 32\right)}. $$ This is related to the results of Gao and Vitale
[Discrete Comput. Geom.} 26 (2001), Elect. Comm. Probab. 8 (2003)] who
considered a similar question for functions with a restriction on the
total variation instead of the Lipschitz constant. Using the results of
Gao and Vitale we give a new proof of the formula for the expected volume
of the convex hull of the $d$-dimensional Brownian motion which is due to
Eldan [Elect. J. Probab., to appear]. Additionally, we prove an analogue
of Eldan's result for the Brownian bridge. Similarly, we show that the
results on the intrinsic volumes of the Lipschitz balls can be translated
into formulae for the expected volumes of zonoids (Aumann integrals)
generated by the Brownian motion and the Brownian bridge. Our proofs
exploit Sudakov's and Tsirelson's theorems which establish a connection
between the intrinsic volumes and the isonormal Gaussian process.
Archive classification: math.PR math.FA math.MG
Mathematics Subject Classification: Primary, 60D05, secondary, 60G15,
52A22
Remarks: 23 pages
Submitted from: sachar.k at gmx.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.6113
or
http://arXiv.org/abs/1404.6113
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sean Li
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:47:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Markov convexity and
nonembeddability of the Heisenberg group" by Sean Li.
Abstract: We compute the Markov convexity invariant of the continuous
Heisenberg group $\mathbb{H}$ to show that it is Markov 4-convex and
cannot be Markov $p$-convex for any $p < 4$. As Markov convexity is a
biLipschitz invariant and Hilbert space is Markov 2-convex, this gives
a different proof of the classical theorem of Pansu and Semmes that
the Heisenberg group does not admit a biLipschitz embedding into any
Euclidean space.
The Markov convexity lower bound will follow from exhibiting an
explicit embedding of Laakso graphs $G_n$ into $\mathbb{H}$ that has
distortion at most $C n^{1/4} \sqrt{\log n}$. We use this to show that
if $X$ is a Markov $p$-convex metric space, then balls of the discrete
Heisenberg group $\mathbb{H}(\mathbb{Z})$ of radius $n$ embed into
$X$ with distortion at least some constant multiple of $$\frac{(\log
n)^{\frac{1}{p}-\frac{1}{4}}}{\sqrt{\log \log n}}.$$ Finally, we show
somewhat unexpectedly that the optimal distortion of embeddings of binary
trees $B_m$ into the infinite dimensional Heisenberg group is on the
order of $\sqrt{\log m}$
Archive classification: math.MG math.FA
Remarks: 20 pages
Submitted from: seanli at math.uchicago.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.6751
or
http://arXiv.org/abs/1404.6751
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Deping Ye
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:49:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Dual Orlicz-Brunn-Minkowski theory:
Orlicz $\varphi$-radial addition, Orlicz $L_{\phi}$-dual mixed volume
and related inequalities" by Deping Ye.
Abstract: This paper develops basic setting for the dual
Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz $\varphi$-radial
addition of two or more star bodies is proposed and related dual
Orlicz-Brunn-Minkowski inequality is established. Based on a linear
Orlicz $\varphi$-radial addition of two star bodies, we derive a
formula for the Orlicz $L_{\phi}$-dual mixed volume. Moreover, a dual
Orlicz-Minkowski inequality for the Orlicz $L_{\phi}$-dual mixed volume,
a dual Orlicz isoperimetric inequality for the Orlicz $L_{\phi}$-dual
surface area and a dual Orlicz-Urysohn inequality for the Orlicz
$L_{\phi}$-harmonic mean radius are proved.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 53A15
Submitted from: deping.ye at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.6991
or
http://arXiv.org/abs/1404.6991
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Narutaka Ozawa and Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:50:44 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A continuum of $\mathrm{C}^*$-norms
on $\IB(H)\otimes \IB(H)$ and related tensor products" by Narutaka Ozawa
and Gilles Pisier.
Abstract: For any pair $M,N$ of von Neumann algebras such that
the algebraic tensor product $M\otimes N$ admits more than one
$\mathrm{C}^*$-norm, the cardinal of the set of $\mathrm{C}^*$-norms is
at least $ {2^{\aleph_0}}$. Moreover there is a family
with cardinality $ {2^{\aleph_0}}$ of injective tensor product functors
for $\mathrm{C}^*$-algebras in Kirchberg's sense.
Let $\IB=\prod_n M_{n}$. We also show that, for any non-nuclear von
Neumann algebra $M\subset \IB(\ell_2)$, the set of $\mathrm{C}^*$-norms
on $\IB \otimes M$ has
cardinality equal to $2^{2^{\aleph_0}}$.
Archive classification: math.OA
Submitted from: pisier at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.7088
or
http://arXiv.org/abs/1404.7088
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stanislaw Kwapien, Mark Veraar, and Lutz
Weis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 2 May 2014 09:52:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$R$-boundedness versus
$\gamma$-boundedness" by Stanislaw Kwapien, Mark Veraar, and Lutz Weis.
Abstract: It is well-known that in Banach spaces with finite cotype, the
$R$-bounded and $\gamma$-bounded families of operators coincide. If in
addition $X$ is a Banach lattice, then these notions can be expressed as
square function estimates. It is also clear that $R$-boundedness implies
$\gamma$-boundedness. In this note we show that all other possible
inclusions fail. Furthermore, we will prove that $R$-boundedness is stable
under taking adjoints if and only if the underlying space is $K$-convex.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 47B99 (Primary) 46B09, 46B07, 47B10
(Secondary)
Submitted from: m.c.veraar at tudelft.nl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1404.7328
or
http://arXiv.org/abs/1404.7328
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Karl-Mikael Perfekt
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 May 2014 14:37:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Weak compactness of operators
acting on o-O type spaces" by Karl-Mikael Perfekt.
Abstract: We consider operators T : M_0 -> Z and T : M -> Z, where Z is
a Banach space and (M_0, M) is a pair of Banach spaces belonging to a
general construction in which M is defined by a "big-O" condition and
M_0 is given by the corresponding "little-o" condition. The main result
characterizes the weakly compact operators T in terms of a certain norm
naturally attached to M, weaker than the M-norm. Further, we develop a
method to extract c_0-subsequences from sequences in M_0. Applications
are given to the characterizations of the weakly compact composition and
Volterra-type integral operators on weighted spaces of analytic functions,
BMOA, VMOA, and the Bloch space.
Archive classification: math.FA math.CV
Remarks: 12 pages
Submitted from: karlmikp at math.ntnu.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.0502
or
http://arXiv.org/abs/1405.0502
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander Koldobsky and Artem Zvavitch
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 May 2014 14:38:41 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An isomorphic version of the
Busemann-Petty problem for arbitrary measures" by Alexander Koldobsky
and Artem Zvavitch.
Abstract: We prove the following theorem. Let $\mu$ be a measure on
$R^n$ with even continuous density, and let $K,L$ be origin-symmetric
convex bodies in $R^n$ so that $\mu(K\cap H)\le \mu(L\cap H)$ for any
central hyperplane H. Then $\mu(K)\le \sqrt{n} \mu(L).$ We also prove
this result with better constants for some special classes of measures
and bodies. Finally, we prove a version of the hyperplane inequality
for convex measures.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A20
Submitted from: koldobskiya at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.0567
or
http://arXiv.org/abs/1405.0567
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alexander V. Kolesnikov and Emanuel Milman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 May 2014 14:40:25 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Remarks on the KLS conjecture and
Hardy-type inequalities" by Alexander V. Kolesnikov and Emanuel Milman.
Abstract: We generalize the classical Hardy and Faber-Krahn inequalities
to arbitrary functions on a convex body $\Omega \subset \mathbb{R}^n$,
not necessarily vanishing on the boundary $\partial \Omega$. This reduces
the study of the Neumann Poincar\'e constant on $\Omega$ to that of the
cone and Lebesgue measures on $\partial \Omega$; these may be bounded
via the curvature of $\partial \Omega$. A second reduction is obtained to
the class of harmonic functions on $\Omega$. We also study the relation
between the Poincar\'e constant of a log-concave measure $\mu$ and
its associated K. Ball body $K_\mu$. In particular, we obtain a simple
proof of a conjecture of Kannan--Lov\'asz--Simonovits for unit-balls of
$\ell^n_p$, originally due to Sodin and Lata{\l}a--Wojtaszczyk.
Archive classification: math.SP math.FA
Remarks: 18 pages
Submitted from: emanuel.milman at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.0617
or
http://arXiv.org/abs/1405.0617
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergey Astashkin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 May 2014 14:41:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Disjointly homogeneous
rearrangement invariant spaces via interpolation" by Sergey Astashkin.
Abstract: A Banach lattice E is called p-disjointly homogeneous, 1< p<
infty, when every sequence of pairwise disjoint normalized elements in E
has a subsequence equivalent to the unit vector basis of l_p. Employing
methods from interpolation theory, we clarify which rearrangement
invariant (r.i.) spaces on [0,1] are p-disjointly homogeneous. In
particular, for every 1<p< infty and any increasing concave function
f on [0,1], which is not equivalent neither 1 nor t, there exists
a p-disjointly homogeneous r.i. space with the fundamental function
f. Moreover, in the class of all interpolation r.i. spaces with respect
to the Banach couple of Lorentz and Marcinkiewicz spaces with the same
fundamental function, dilation indices of which are non-trivial, for
every 1<p< infty, there is only a unique p-disjointly homogeneous space.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B03, 46B70
Remarks: 23 pages
Submitted from: astash at samsu.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.0681
or
http://arXiv.org/abs/1405.0681
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Deping Ye
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 May 2014 14:43:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Dual Orlicz-Brunn-Minkowski theory:
dual Orlicz $L_{\phi}$ affine and geominimal surface areas" by Deping Ye.
Abstract: This paper aims to develop basic theory for the dual Orlicz
$L_{\phi}$ affine and geominimal surface areas for star bodies, which
are dual to the Orlicz $L_{\phi}$ affine and geominimal surface areas for
convex bodies (Ye, arXiv:1403.1643). These new affine invariants belong
to the recent dual Orlicz-Brunn-Minkowski theory for star bodies (Ye,
arXiv:1404.6991). Basic properties for these new affine invariants will
be provided. Moreover, related Orlicz affine isoperimetric inequality,
cyclic inequality, Santal\'{o} style inequality and Alexander-Fenchel type
inequality are established. Besides, an Orlicz isoperimetric inequality
for the Orlicz $\phi$-surface area and an Orlicz-Urysohn inequality for
the Orlicz $\phi$ mean width are given.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A20, 53A15
Submitted from: deping.ye at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.0746
or
http://arXiv.org/abs/1405.0746
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by N. Albuquerque, D. Nunez-Alarcon and D. M.
Serrano-Rodríguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 May 2014 14:45:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A subexponential vector-valued
Bohnenblust-Hille type inequality" by N. Albuquerque, D. Nunez-Alarcon
and D. M. Serrano-Rodríguez.
Abstract: Bayart, Pellegrino and Seoane recently proved that the
polynomial Bohnenblust--Hille inequality for complex scalars is
subexponential. We show that a vector valued polynomial Bohnenblust-Hille
inequality on complex Banach lattices is also subexponential for some
special cases. Our main result result recovers the best known constants
of the classical polynomial inequality provided in \cite{bps}.
Archive classification: math.FA
Submitted from: ngalbqrq at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.1204
or
http://arXiv.org/abs/1405.1204
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grzegorz Plebanek and Damian Sobota
m: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 15 May 2014 14:47:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Countable tightness in the spaces
of regular probability measures" by Grzegorz Plebanek and Damian Sobota.
Abstract: We prove that if $K$ is a compact space and the space $P(K\times
K)$ of regular probability measures on $K\times K$ has countable tightness
in its $weak^*$ topology, then $L_1(\mu)$ is separable for every $\mu\in
P(K)$. It has been known that such a result is a consequence of Martin's
axiom MA$(\omega_1)$.
Our theorem has several consequences; in particular, it generalizes
a theorem due to Bourgain and Todor\v{c}evi\'c on measures on Rosenthal
compacta.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46E15, 46E27, 54C35
Remarks: 9 pages
Submitted from: grzes at math.uni.wroc.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.2527
or
http://arXiv.org/abs/1405.2527
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Message concerning the death of Manuel Valdivia
Date: Thu, 22 May 2014 08:42:41 -0500
To: banach at math.okstate.edu
From: Dale Alspach <alspach at math.okstate.edu>
---------------------------------
Prof. Manuel Valdivia passed away April the 29th, 2014. He was member of
the Spanish Academy of Sciences, professor at the Universitat de Valencia
(Spain) and the Universidad Politecnica de Valencia (Spain), and Dr.
Honoris Causa at various universities. Author of almost 200 research papers
and several books in Functional Analysis, he was one of the outstanding
mathematicians in Spain.
Condolence messages may be sent to manuelvaldivia2014 at gmail.com
Vicente Montesinos
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Third Announcement of BWB 2014
Date: Mon, 26 May 2014 18:20:09 -0300
To: banach at math.okstate.edu
From: valentin ferenczi <ferenczi.math at gmail.com>
THIRD ANNOUNCEMENT OF BWB 2014
First Brazilian Workshop in Geometry of Banach Spaces
August 25-29, 2014
Maresias, Sao Paulo State, Brazil.
This is the third announcement for the First Brazilian Workshop in
Geometry of Banach Spaces, organized by the University of Sao Paulo
(USP), in the week August 25-29, 2014, at the Beach Hotel Maresias, on
the coast of Sao Paulo State, in Maresias.
We would like to recall that the ABSTRACT SUBMISSION deadline, MAY
31st, expires in a few days. Deadline for registration is June 30th.
Please access the website of the conference:
http://www.ime.usp.br/~banach/bwb2014/
Please CHECK the VISA SITUATION related to your travel document, as
requirements for visa depend on bilateral relations between the two
countries. For example, participants travelling with a US passport
will need a visa.
Please consult the website for all information and contact us at
bwb2014 at gmail.com if you have any question.
Plenary speakers:
S. A. Argyros (Nat. Tech. U. Athens)
P. Dodos (U. Athens)
G. Godefroy (Paris 6)
W. B. Johnson (Texas A&M)
P. Hayek (Czech Acad. & Cz. Polytech. U.)
P. Koszmider (Polish Acad. Warsaw)
C. Rosendal (U. Illinois Chicago)
G. Schechtman (Weizmann Inst.)
Th. Schlumprecht (Texas A&M)
S. Todorcevic (CNRS Paris & U. Toronto)
Scientific committee
J. M. F. Castillo (U. Extremadura)
V. Ferenczi (U. São Paulo, chair)
R. Haydon (U. Oxford)
W. B. Johnson (Texas A&M)
G. Pisier (Paris 6 & Texas A&M)
Th. Schlumprecht (Texas A&M)
S. Todorcevic (CNRS Paris & U. Toronto)
The organizers,
F. Baudier, C. Brech, V. Ferenczi, E. M. Galego, and J. Lopez-Abad.
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Fall School ''Metric Embeddings: Constructions and Obstructions''
Date: Mon, 02 Jun 2014 20:26:43 -0000
To: "banach at www.math.okstate.edu" <banach at math.okstate.edu>
From: BAUDIER Florent <florent.baudier at imj-prg.fr>
Dear Colleagues,
We are looking for PhD students, postdocs or very young
researchers that might be interested in being an active participant of the
Fall
School ''Metric Embeddings: Constructions and Obstructions'',
that we will be organizing in Paris, 3-7 November 2014. The scientific
committee will select 12 active participants from the pool of applicants.
The deadline to apply is June 30, 2014. The description of the school,
its organization and the application and selection processes are fully
explained on the website of the Fall School.
http://www.math.tamu.edu/~florent/fallschool.html
The accommodation in Paris of an active participant will be fully taken
care off and we should be able to partially (and eventually fully) cover
its
travel expenses.
Feel free to spread the word to whom you think might be interested.
Feel free also, to email us for additional information at
florent.baudier at imj-p
rg.fr
The organizing committee,
F. Baudier (Institut de Mathematiques de Jussieu-Paris Rive Gauche and
Texas A&M University)
G. Godefroy (Institut de Mathematiques de Jussieu-Paris Rive Gauche,
CNRS)
P. Pansu (Universite Paris-Sud 11)
R. Tessera (Universite Paris-Sud 11, CNRS)
_______________________________________________
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Banach at www.math.okstate.edu
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Subject: [Banach] Informal Analysis and Probability Seminar, October 17-19, 2014
Date: Wed, 11 Jun 2014 04:25:28 -0400
To: banach at math.okstate.edu
From: zvavitch at math.kent.edu
Dear Colleague,
Analysis/Probability group at the University of Michigan,
and the Analysis group at Kent State University are happy to announce
a meeting of the Informal Analysis and Probability Seminar, which will
run at the Department of Mathematics at University of Michigan October
17-19, 2014.
The plenary lecture series will be given by:
Olivier Guedon (Pairs-Est University and University of Michigan),
and
Fedor Nazarov (Kent State)
Each speaker will deliver a four hour lecture series designed to be
accessible for graduate students.
Funding is available to cover the local expenses, and possibly travel
expenses, of a limited number of participants. Graduate students,
postdoctoral researchers, and members of underrepresented groups are
particularly encouraged to apply for support.
Further information, and an online registration form, can be found
online http://dept.math.lsa.umich.edu/conferences/informalAnalysis/.
We encourage you to register as soon as possible, but to receive a support
and/or help with hotel reservation, please, do register before September
5, 2014.
Please feel free to contact us at rudelson at umich.edu / romanv at umich.edu
for any further information.
Sincerely,
Analysis/Probability group at the University of Michigan,
and the Analysis group at Kent State University
_______________________________________________
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Banach at www.math.okstate.edu
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Subject: Abstract of a paper by A. Jimenez-Vargas
Date: Mon, 16 Jun 2014 13:13:13 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Weakly compact composition
operators on spaces of Lipschitz functions" by A. Jimenez-Vargas.
Abstract: Let $X$ be a pointed compact metric space. Assuming that
$\mathrm{lip}_0(X)$ has the uniform separation property, we prove that
every weakly compact composition operator on spaces of Lipschitz functions
$\mathrm{Lip}_0(X)$ and $\mathrm{lip}_0(X)$ is compact.
Archive classification: math.FA
Mathematics Subject Classification: 47B33, 47B07, 26A16
Remarks: 6 pages
Submitted from: ajimenez at ual.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.4267
or
http://arXiv.org/abs/1405.4267
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by T. Kappeler, A. Savchuk, A. Shkalikov, and P. Topalov
Date: Mon, 16 Jun 2014 13:15:24 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Interpolation of nonlinear maps"
by T. Kappeler, A. Savchuk, A. Shkalikov, and P. Topalov.
Abstract: Let $(X_0, X_1)$ and $(Y_0, Y_1)$ be complex Banach couples
and assume that $X_1\subseteq X_0$ with norms satisfying $\|x\|_{X_0}
\le c\|x\|_{X_1}$ for some $c > 0$. For any $0<\theta <1$, denote by
$X_\theta = [X_0, X_1]_\theta$ and $Y_\theta = [Y_0, Y_1]_\theta$ the
complex interpolation spaces and by $B(r, X_\theta)$, $0 \le \theta \le
1,$ the open ball of radius $r>0$ in $X_\theta$, centered at zero. Then
for any analytic map $\Phi: B(r, X_0) \to Y_0+ Y_1$ such that $\Phi:
B(r, X_0)\to Y_0$ and $\Phi: B(c^{-1}r, X_1)\to Y_1$ are continuous and
bounded by constants $M_0$ and $M_1$, respectively, the restriction
of $\Phi$ to $B(c^{-\theta}r, X_\theta)$, $0 < \theta < 1,$ is shown
to be a map with values in $Y_\theta$ which is analytic and bounded by
$M_0^{1-\theta} M_1^\theta$.
Archive classification: math.FA
Submitted from: p.topalov at neu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.4253
or
http://arXiv.org/abs/1405.4253
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S Dutta and D Khurana
Date: Mon, 16 Jun 2014 13:17:40 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Ordinal indices for complemented
subspaces of l_p" by S Dutta and D Khurana.
Abstract: We provide complete isomorphic invariance of a class of
translation invariant complemented subspaces of L_p constructed by
Bourgain, Rosenthal and Schechtman. We compute ordinal L_p-indices
for this class. We further show that the isometric index of a tree
subspace over a well founded tree is an invariance for the order of the
tree. Finally we provide a dichotomy for the subspaces of L_p with small
ordinal indices.
Archive classification: math.FA
Submitted from: divyakhurana11 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.4499
or
http://arXiv.org/abs/1405.4499
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eusebio Gardella and Hannes Thiel
Date: Mon, 16 Jun 2014 13:20:06 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Banach algebras generated by an
invertible isometry of an $L^p$-space" by Eusebio Gardella and Hannes
Thiel.
Abstract: We study and classify Banach algebras that are generated by
an invertible isometry of an $L^p$-space together with its inverse. We
associate to each such isometry a spectral invariant which contains
considerably more information than its spectrum as an operator. We show
that this invariant describes the isometric isomorphism type of the
Banach algebra that the isometry generates together with its inverse.
In the case of invertible isometries with full spectrum, these Banach
algebras parametrize all completions of the group algebra
$\mathbb{C}[\mathbb{Z}]$ corresponding to unital, contractive
representations on $L^p$-spaces. The extreme cases are the algebra of
$p$-pseudofunctions on $\mathbb{Z}$, and the commutative $C^*$-algebra
$C(S^1)$. Moreover, there are uncountably many non-isometrically
isomorphic "intermediate" algebras, all of which are shown to be closed
under continuous functional calculus.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary: 46J40, 46H35. Secondary:
47L10
Remarks: 43 pages
Submitted from: gardella at uoregon.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.5589
or
http://arXiv.org/abs/1405.5589
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Cwikel, Mario Milman and Richard Rochberg
Date: Mon, 16 Jun 2014 13:21:34 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Nigel Kalton and the interpolation
theory of commutators" by Michael Cwikel, Mario Milman and Richard
Rochberg.
Abstract: This is the second of a series of papers surveying some
small part of the remarkable work of our friend and colleague Nigel
Kalton. We have written it as part of a tribute to his memory. It does
not contain new results. One of the many topics in which Nigel made
very significant and profound contributions deals with commutators in
interpolation theory. It was our great privilege to work with him on one
of his many papers about this topic. Our main purpose here is to offer}
an introduction to that paper: A unified theory of commutator estimates
for a class of interpolation methods. Adv. Math. 169 (2002), no. 2,
241--312. We sketch the theory of interpolation spaces constructed
using pseudolattices which was developed in that paper and which enables
quite general formulation of commutator theorems. We seek to place the
results of that paper in the general context of preceding and subsequent
research on this topic, also indicating some applications to other fields
of analysis and possible directions for future research.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B70, Secondary 42B20,
42B30, 46B42, 42B37, 35J60
Remarks: 16 pages
Submitted from: mcwikel at math.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.5686
or
http://arXiv.org/abs/1405.5686
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania and Niels Jakob Laustsen
Date: Mon, 16 Jun 2014 13:25:31 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Uniqueness of the maximal ideal
of operators on the $\ell_p$-sum of $\ell_\infty^n\ (n\in\mathbb{N})$
for $1<p<\infty$" by Tomasz Kania and Niels Jakob Laustsen.
Abstract: A recent result of Leung (Proceedings of the American
Mathematical Society, to appear) states that the Banach algebra
$\mathscr{B}(X)$ of bounded, linear operators on the Banach space
$X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_1}$
contains a unique maximal ideal. We show that
the same conclusion holds true for the Banach spaces
$X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_\infty^n\bigr)_{\ell_p}$ and
$X=\bigl(\bigoplus_{n\in\mathbb{N}}\ell_1^n\bigr)_{\ell_p}$ whenever
$p\in(1,\infty)$.
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/1405.5715
or
http://arXiv.org/abs/1405.5715
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Will Grilliette
Date: Mon, 16 Jun 2014 13:27:19 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Matricial Banach spaces" by
Will Grilliette.
Abstract: This work performs a study of the category of complete
matrix-normed spaces, called matricial Banach spaces. Many of the usual
constructions of Banach spaces extend in a natural way to matricial
Banach spaces, including products, direct sums, and completions. Also,
while the minimal matrix-norm on a Banach space is well-known, this work
characterizes the maximal matrix-norm on a Banach space from the work
of Effros and Ruan as a dual operator space.
Moreover, building from the work of Blecher, Ruan, and Sinclair, the
Haagerup tensor product is merged with the direct sum to form a Haagerup
tensor algebra, which shares the analogous universal property of the
Banach tensor algebra from the work of Leptin.
Archive classification: math.FA
Mathematics Subject Classification: 46M99
Remarks: 19 pages
Submitted from: w.b.grilliette at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.5951
or
http://arXiv.org/abs/1405.5951
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Paata Ivanisvili, Dmitriy M. Stolyarov, and Pavel B. Zatitskiy
Date: Mon, 16 Jun 2014 13:29:25 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Bellman VS Beurling: sharp
estimates of uniform convexity for $L^p$ spaces" by Paata Ivanisvili,
Dmitriy M. Stolyarov, and Pavel B. Zatitskiy.
Abstract: We obtain the classical Hanner inequalities by the Bellman
function method. These inequalities give sharp estimates for the moduli
of convexity of Lebesgue spaces. Easy ideas from differential geometry
help us to find the Bellman function using neither ``magic guesses''
nor calculations.
Archive classification: math.CA math.DG math.FA
Remarks: 11 pages
Submitted from: dms at pdmi.ras.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.6229
or
http://arXiv.org/abs/1405.6229
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Maria D. Acosta
Date: Mon, 16 Jun 2014 13:30:55 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "The Bishop-Phelps-Bollob\'{a}s
property for operators on $C(K)$" by Maria D. Acosta.
Abstract: We provide a version for operators of the
Bishop-Phelps-Bollob\'{a}s Theorem when the domain space is the
complex space $C_0(L)$. In fact we prove that the space of weakly
compact operators from the complex space $C_0(L)$ into a ${\mathbb
C}$-uniformly convex space satisfies the Bishop-Phelps-Bollob\'{a}s
property for operators. As a consequence, in the complex case, the
space of operators from $C_0(L)$ into $L_p (\mu)$ ($1 \le p < \infty $)
satisfies the Bishop-Phelps-Bollob\'{a}s property for operators.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B28, 47B99
Submitted from: dacosta at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1405.6428
or
http://arXiv.org/abs/1405.6428
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Herve Queffelec, and Kristian Seip
Date: Mon, 16 Jun 2014 13:33:06 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Approximation numbers of
composition operators on $H^p$ spaces of Dirichlet series" by Herve
Queffelec, and Kristian Seip.
Abstract: By a theorem of Bayart, $\varphi$ generates a bounded
composition operator on the Hardy space $\Hp$of Dirichlet series
($1\le p<\infty$) only if $\varphi(s)=c_0 s+\psi(s)$, where $c_0$ is
a nonnegative integer and $\psi$ a Dirichlet series with the following
mapping properties: $\psi$ maps the right half-plane into the half-plane
$\Real s >1/2$ if $c_0=0$ and is either identically zero or maps the
right half-plane into itself if $c_0$ is positive. It is shown that
the $n$th approximation numbers of bounded composition operators on
$\Hp$ are bounded below by a constant times $r^n$ for some $0<r<1$ when
$c_0=0$ and bounded below by a constant times $n^{-A}$ for some $A>0$
when $c_0$ is positive. Both results are best possible. Estimates rely on
a combination of soft tools from Banach space theory ($s$-numbers, type
and ecotype of Banach spaces, Weyl inequalities, and Schauder bases) and
a certain interpolation method for $\Ht$, developed in an earlier paper,
using estimates of solutions of the $\overline{\partial}$ equation. A
transference principle from $H^p$ of the unit disc is discussed,
leading to explicit examples of compact composition operators on $\Ho$
with approximation numbers decaying at a variety of sub-exponential rates.
Archive classification: math.FA math.CV
Submitted from: seip at math.ntnu.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.0445
or
http://arXiv.org/abs/1406.0445
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hana Bendova, Ondrej F.K. Kalenda and Jiri Spurny
Date: Mon, 16 Jun 2014 13:35:24 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Quantification of the Banach-Saks
property" by Hana Bendova, Ondrej F.K. Kalenda and Jiri Spurny.
Abstract: We investigate possible quantifications of the Banach-Saks
property and the weak Banach-Saks property. We prove quantitative
versions of relationships of the Banach-Saks property of a set with norm
compactness and weak compactness. We further establish a quantitative
version of the characterization of the weak Banach-Saks property of a
set using uniform weak convergence and $\ell_1$-spreading models. We
also study the case of the unit ball and in this case we prove a
dichotomy which is an analogue of the James distortion theorem for
$\ell_1$-spreading models.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
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/1406.0684
or
http://arXiv.org/abs/1406.0684
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii
Date: Mon, 16 Jun 2014 13:37:11 -0500
To: alspach at math.okstate.edu, banach at math.okstate.edu
From: alspach at math.okstate.edu (Dale Alspach)
This is an announcement for the paper "Connections between metric
characterizations of superreflexivity and Radon-Nikod\'ym property for
dual Banach spaces" by Mikhail I. Ostrovskii.
Abstract: Johnson and Schechtman (2009) characterized superreflexivity
in terms of finite diamond graphs. The present author characterized
the Radon-Nikod\'ym property (RNP) for dual spaces in terms of the
infinite diamond. This paper is devoted to further study of relations
between metric characterizations of superreflexivity and the RNP for
dual spaces. The main result is that finite subsets of any set $M$
whose embeddability characterizes the RNP for dual spaces, characterize
superreflexivity. It is also observed that the converse statement does
not hold, and that $M=\ell_2$ is a counterexample.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B85 (primary), 46B07, 46B22
(secondary)
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.0904
or
http://arXiv.org/abs/1406.0904
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] School and conference 2nd announcement: Besancon, Autumn 2014
Date: Thu, 26 Jun 2014 18:37:50 +0200
To: banach at math.okstate.edu, gdr_afhp at listes.math.cnrs.fr
From: Tony Prochazka <antonin.prochazka at univ-fcomte.fr>
Dear colleagues,
This is the second annoncement of the two following closely related events.
1) The *Autum school on "Nonlinear geometry of Banach spaces and
applications"*, in Metabief, France (October 20-24, 2014). The following
mathematicians have kindly accepted our invitation to deliver a short
course: Gilles Godefroy (Université Paris 6), Petr Hajek (Czech Academy of
Sciences and Czech Technical University), Mikhail Ostrovskii (St. John's
University, New York), Nirina Lovasoa Randrianarivony (Saint Louis
University - to be confirmed), Guoliang Yu (Texas A&M University).
Web:
http://trimestres-lmb.univ-fcomte.fr/Autumn-School-on-Nonlinear.html?lang=en
Registration: Open until September 5.
2) The *conference on "Geometric functional analysis and its applications"*
in Besancon, France (October 27-31, 2014). The following main speakers have
already agreed to deliver a plenary lecture: Fernando Albiac (Univ. Publica
de Navarra), Florent Baudier (Texas A&M University, Paris 6) , Robert
Deville (Univ. Bordeaux) , Stephen Dilworth (Univ. South Carolina),
Valentin Ferenczi (Univ. Sao Paulo) , Bill Johnson (Texas A&M University),
Beata Randrianantoanina (Miami Univ Ohio), Gideon Schechtman (Weizmann
Institute), Thomas Schlumprecht (Texas A&M University), Alain Valette
(Univ. Neuchatel).
Web:
http://trimestres-lmb.univ-fcomte.fr/Autumn-School-on-Nonlinear.html?lang=en
Registration: Open until September 30.
Participants will have the opportunity to give a short talk. The deadline
for abstract submission is September 20.
The purpose of these meetings is to bring together researchers and students
with common interest in the field. They will offer many possibilities for
informal discussions. Graduate students and others beginning their
mathematical career are encouraged to participate.
Thes two events are part of the trimester on "Geometric and noncommutative
methods in functional analysis" organized by the "Laboratoire de
Mathematiques de Besancon" during the Autumn 2014, see
http://trimestres-lmb.univ-fcomte.fr/af.html .
We are looking forward to meeting you!
The organizers,
Gilles Lancien and Tony Prochazka
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
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Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Amir Bahman Nasseri
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:16:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The spectrum of operators on C(K)
with the Grothendieck Property and characterization of J-class operators
which are adjoints" by Amir Bahman Nasseri.
Abstract: This article deals with properties of spectra of operators
on C(K)-spaces with the Grothendieck property (e.g. l^{\infty}) and
application to so called J-class operators introduced by A. Manoussos
and G. Costakis. We will show that C(K) has the Grothendieck property
if and only if the boundary of the spectrum of every operator on C(K)
consists entirely of eigenvalues of its adjoint. As a consequence we
will see that there does not exist invertible J-class operators on C(K)
with the Grothendieck property. In the third section we will give a
quantitative and qualitative characterization of all J-class operators
on l^{\infty} which are adjoints from operators on l^1.
Archive classification: math.SP math.DS math.FA
Remarks: 19 pages
Submitted from: nasseri at uni-wuppertal.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.3815
or
http://arXiv.org/abs/1406.3815
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Cwikel, Mario Milman and Richard
Rochberg
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:18:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A brief survey of Nigel Kalton's
work on interpolation and related topics" by Michael Cwikel, Mario
Milman and Richard Rochberg.
Abstract: This is the third of a series of papers surveying some small
part of the remarkable work of our friend and colleague Nigel Kalton. We
have written it as part of a tribute to his memory. It does not contain
new results. This time, rather than concentrating on one particular paper,
we attempt to give a general overview of Nigel's many contributions to
the theory of interpolation of Banach spaces, and also, significantly,
quasi-Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B70, 46A16. Secondary
42B20, 42B30
Remarks: 11 pages
Submitted from: mcwikel at math.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.3842
or
http://arXiv.org/abs/1406.3842
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Astashkin, F. Sukochev, and D. Zanin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:20:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On uniqueness of distribution
of a random variable whose independent copies span a subspace in L_p"
by S. Astashkin, F. Sukochev, and D. Zanin.
Abstract: Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space
of all (classes of) p-integrable functions on [0,1]. It is known that a
sequence of independent copies of a mean zero random variable f from L_p
spans in L_p a subspace isomorphic to some Orlicz sequence space l_M. We
present precise connections between M and f and establish conditions
under which the distribution of a random variable f whose independent
copies span l_M in L_p is essentially unique.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B09
Remarks: 14 pages, submitted
Submitted from: astash at samsu.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.4950
or
http://arXiv.org/abs/1406.4950
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Khalil Saadi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:29:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some properties for Lipschitz
strongly p-summing operators" by Khalil Saadi.
Abstract: We consider the space of molecules endowed with the transpose
version of the Chevet-Saphar norm and we identify its dual space with
the space of Lipschitz strongly p-summing operators. We also extend
some old results to the category of Lipschitz mappings and we give a
factorization result of Lipschitz (p,r,s)-summing operators.
Archive classification: math.FA
Mathematics Subject Classification: [2000] 47B10, 46B28, 47L20
Remarks: 19 pages
Submitted from: kh_saadi at yahoo.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.5551
or
http://arXiv.org/abs/1406.5551
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: Mon, 30 Jun 2014 13:37:25 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Tukey classification of some
ideals in $\omega$ and the lattices of weakly compact sets in Banach
spaces" by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez.
Abstract: We study the lattice structure of the family of weakly
compact subsets of the unit ball $B_X$ of a separable Banach space $X$,
equipped with the inclusion relation (this structure is denoted by
$\mathcal{K}(B_X)$) and also with the parametrized family of almost
inclusion relations $K \subseteq L+\epsilon B_X$, where $\epsilon>0$
(this structure is denoted by $\mathcal{AK}(B_X)$). Tukey equivalence
between partially ordered sets and a suitable extension to deal with
$\mathcal{AK}(B_X)$ are used. Assuming the axiom of analytic determinacy,
we prove that separable Banach spaces fall into four categories,
namely: $\mathcal{K}(B_X)$ is equivalent either to a singleton,
or to $\omega^\omega$, or to the family $\mathcal{K}(\mathbb{Q})$
of compact subsets of the rational numbers, or to the family
$[\mathfrak{c}]^{<\omega}$ of all finite subsets of the continuum. Also
under the axiom of analytic determinacy, a similar classification
of $\mathcal{AK}(B_X)$ is obtained. For separable Banach spaces not
containing $\ell^1$, we prove in ZFC that $\mathcal{K}(B_X) \sim
\mathcal{AK}(B_X)$ are equivalent to either $\{0\}$, $\omega^\omega$,
$\mathcal{K}(\mathbb{Q})$ or $[\mathfrak{c}]^{<\omega}$. The lattice
structure of the family of all weakly null subsequences of an
unconditional basis is also studied.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 46B20(Primary), 03E60, 03E75, 06A06,
46B50, 03E75
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.5526
or
http://arXiv.org/abs/1406.5526
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Javier Alejandro Chavez-Dominguez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:39:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lipschitz $p$-convex and
$q$-concave maps" by Javier Alejandro Chavez-Dominguez.
Abstract: The notions of $p$-convexity and $q$-concavity are
mostly known because of their importance as a tool in the study of
isomorphic properties of Banach lattices, but they also play a role
in several results involving linear maps between Banach spaces and
Banach lattices. In this paper we introduce Lipschitz versions of these
concepts, dealing with maps between metric spaces and Banach lattices,
and start by proving nonlinear versions of two well-known factorization
theorems through $L_p$ spaces due to Maurey/Nikishin and Krivine. We also
show that a Lipschitz map from a metric space into a Banach lattice is
Lipschitz $p$-convex if and only if its linearization is $p$-convex.
Furthermore, we elucidate why there is such a close relationship
between the linear and nonlinear concepts by proving characterizations
of Lipschitz $p$-convex and Lipschitz $q$-concave maps in terms of
factorizations through $p$-convex and $q$-concave Banach lattices,
respectively, in the spirit of the work of Raynaud and Tradacete.
Archive classification: math.FA
Remarks: 25 pages
Submitted from: jachavezd at math.utexas.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.6357
or
http://arXiv.org/abs/1406.6357
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Javier Alejandro Chavez-Dominguez and Denka
Kutzarova
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:42:04 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stability of low-rank matrix
recovery and its connections to Banach space geometry" by Javier Alejandro
Chavez-Dominguez and Denka Kutzarova.
Abstract: There are well-known relationships between compressed sensing
and the geometry of the finite-dimensional $\ell_p$ spaces. A result
of Kashin and Temlyakov can be described as a characterization of the
stability of the recovery of sparse vectors via $\ell_1$-minimization
in terms of the Gelfand widths of certain identity mappings between
finite-dimensional $\ell_1$ and $\ell_2$ spaces, whereas a more recent
result of Foucart, Pajor, Rauhut and Ullrich proves an analogous
relationship even for $\ell_p$ spaces with $p < 1$. In this paper we
prove what we call matrix or noncommutative versions of these results:
we characterize the stability of low-rank matrix recovery via Schatten
$p$-(quasi-)norm minimization in terms of the Gelfand widths of certain
identity mappings between finite-dimensional Schatten $p$-spaces.
Archive classification: math.FA cs.IT math.IT
Remarks: 19 pages, 1 figure
Submitted from: jachavezd at math.utexas.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.6712
or
http://arXiv.org/abs/1406.6712
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Felix Cabello Sanchez, Jesus M. F. Castillo
and Nigel J. Kalton
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:44:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Complex interpolation and twisted
twisted Hilbert spaces" by Felix Cabello Sanchez, Jesus M. F. Castillo
and Nigel J. Kalton.
Abstract: We show that Rochberg's generalizared interpolation spaces
$\mathscr Z^{(n)}$ arising from analytic families of Banach spaces
form exact sequences $0\to \mathscr Z^{(n)} \to \mathscr Z^{(n+k)} \to
\mathscr Z^{(k)} \to 0$. We study some structural properties of those
sequences; in particular, we show that nontriviality, having strictly
singular quotient map, or having strictly cosingular embedding depend
only on the basic case $n=k=1$. If we focus on the case of Hilbert
spaces obtained from the interpolation scale of $\ell_p$ spaces, then
$\mathscr Z^{(2)}$ becomes the well-known Kalton-Peck $Z_2$ space; we
then show that $\mathscr Z^{(n)}$ is (or embeds in, or is a quotient of)
a twisted Hilbert space only if $n=1,2$, which solves a problem posed
by David Yost; and that it does not contain $\ell_2$ complemented unless
$n=1$. We construct another nontrivial twisted sum of $Z_2$ with itself
that contains $\ell_2$ complemented.
Archive classification: math.FA
Mathematics Subject Classification: 46M18, 46B70, 46B20
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.6723
or
http://arXiv.org/abs/1406.6723
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M. F. Castillo, Manuel Gonzalez and
Pier Luigi Papini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:46:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On nested sequences of convex
sets in a Banach space" by Jesus M. F. Castillo, Manuel Gonzalez and
Pier Luigi Papini.
Abstract: In this paper we study different aspects of the representation
of weak*-compact convex sets of the bidual $X^{**}$ of a separable Banach
space $X$ via a nested sequence of closed convex bounded sets of $X$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: This paper is to appear in Studia Mathematica
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.6725
or
http://arXiv.org/abs/1406.6725
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Felix Cabello Sanchez,
Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 30 Jun 2014 13:47:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$\aleph$-injective Banach spaces
and $\aleph$-projective compacta" by Antonio Aviles, Felix Cabello
Sanchez, Jesus M. F. Castillo, Manuel Gonzalez and Yolanda Moreno.
Abstract: A Banach space $E$ is said to be injective if for every Banach
space $X$ and every subspace $Y$ of $X$ every operator $t:Y\to E$ has an
extension $T:X\to E$. We say that $E$ is $\aleph$-injective (respectively,
universally $\aleph$-injective) if the preceding condition holds for
Banach spaces $X$ (respectively $Y$) with density less than a given
uncountable cardinal $\aleph$. We perform a study of $\aleph$-injective
and universally $\aleph$-injective Banach spaces which extends the basic
case where $\aleph=\aleph_1$ is the first uncountable cardinal. When
dealing with the corresponding ``isometric'' properties we arrive to our
main examples: ultraproducts and spaces of type $C(K)$. We prove that
ultraproducts built on countably incomplete $\aleph$-good ultrafilters
are $(1,\aleph)$-injective as long as they are Lindenstrauss spaces. We
characterize $(1,\aleph)$-injective $C(K)$ spaces as those in which the
compact $K$ is an $F_\aleph$-space (disjoint open subsets which are the
union of less than $\aleph$ many closed sets have disjoint closures)
and we uncover some projectiveness properties of $F_\aleph$-spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 54B30, 46B08, 54C15, 46B26
Remarks: This paper is to appear in Revista Matem\'atica Iberoamericana
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.6733
or
http://arXiv.org/abs/1406.6733
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS 2014
Date: Wed, 02 Jul 2014 15:02:32 -0500
To: banach at math.okstate.edu
From: Bill Johnson <johnson at math.tamu.edu>
1st ANNOUNCEMENT OF SUMIRFAS 2014
The Summer Informal Regional Functional Analysis Seminar
July 25-27
Texas A&M University, College Station
The speakers for SUMIRFAS 2014 are
March Boedihardjo Gilles Pisier
Michael Brannan Lova Randrianarivony
Caleb Eckhardt Dan Voiculescu
Matthew Kennedy Deping Ye
Vern Paulsen
The schedule for SUMIRFAS will be posted on the Workshop in Analysis
and Probability webpage:
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 166. 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.
SUMIRFAS will be preceded by a Concentration Week on Free Probability
from July 21 to 25. Topics will include operator algebras, the connections
to random matrix theory, operator-valued and fully matricial techniques,
stochastic processes, limit theorems, and free stochastic differential
equations.
The program will feature lecture series by Greg Anderson, Serban
Belinschi,
and Dimitri Shlyakhtenko. The webpage is located at:
http://www.math.tamu.edu/~jwilliams/Free_Probability_2014
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 Free Probability
contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema
<ken.dykema at math.tamu.edu>, or John Williams <jwilliams at
math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at www.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS 2014
From: Bill Johnson <johnson at math.tamu.edu>
Date: Mon, 21 Jul 2014 12:32:44 -0500 (CDT)
To: banach at math.okstate.edu
2nd ANNOUNCEMENT OF SUMIRFAS 2014
The Summer Informal Regional Functional Analysis Seminar
July 25-27
Texas A&M University, College Station
The speakers for SUMIRFAS 2014 are
March Boedihardjo A new characterization of certain quasidiagonal
operators
Michael Brannan L_p -representations of discrete quantum groups and exotic
quantum group
C*-algebras
Caleb Eckhardt Unitary representations of nilpotent groups and the
structure of the C*-algebras
they generate
Matthew Kennedy Boundaries of reduced C*-algebras of discrete groups
Vern Paulsen Quantum chromatic numbers
Gilles Pisier A continuum of C*-norms on B(H)?B(H) and related tensor
products
Lova Randrianarivony TBA
Dan Voiculsecu Some C*-algebras which are coronas of non-C*-Banach
algebras
Deping Ye Is Einstein's "spooky action" common?
The webpage for SUMIRFAS, including links to the schedule and abstracts,
can
be found at
http://www.math.tamu.edu/~kerr/workshop/sumirfas2014
The first talk will be at 2:00 pm on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 166. 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
SUMIRFAS will be preceded by a Concentration Week on Free Probability
from July 21 to 25. Topics will include operator algebras, the connections
to random matrix theory, operator-valued and fully matricial techniques,
stochastic processes, limit theorems, and free stochastic differential
equations.
The program will feature lecture series by Greg Anderson, Serban
Belinschi,
and Dimitri Shlyakhtenko. The webpage is located at:
http://www.math.tamu.edu/~jwilliams/Free_Probability_2014
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 Free Probability
contact Michael Anshelevich <manshel at math.tamu.edu>, Ken Dykema
<ken.dykema at math.tamu.edu>, or John Williams <jwilliams at
math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at www.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 Said Amana Abdillah, Jean Esterle,
andBernhard Hermann Haak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 12:53:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sur quelques extensions au cadre
Banachique de la notion d'op\'erateur de Hilbert-Schmidt" by Said
Amana Abdillah, Jean Esterle, and Bernhard Hermann Haak.
Abstract: In this work we discuss several ways to extend to the context
of Banach spaces the notion of Hilbert-Schmidt operators: $p$-summing
operators, $\gamma$-summing or $\gamma$-radonifying operators, weakly
$*1$-nuclear operators and classes of operators defined via factorization
properties. We introduce the class $PS_2(E; F)$ of pre-Hilbert-Schmidt
operators as the class of all operators $u:E\to F$ such that $w\circ
u \circ v$ is Hilbert-Schmidt for every bounded operator $v: H_1\to E$
and every bounded operator $w:F\to H_2$, where $H_1$ et $H_2$ are Hilbert
spaces. Besides the trivial case where one of the spaces $E$ or $F$ is a
"Hilbert-Schmidt space", this space seems to have been described only in
the easy situation where one of the spaces $E$ or $F$ is a Hilbert space.
Archive classification: math.FA
Remarks: 18 pages
Submitted from: bernhard.haak at math.u-bordeaux1.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.7546
or
http://arXiv.org/abs/1406.7546
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Slawomir Borzdynski and Andrzej Wisnicki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 12:56:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A common fixed point theorem for
a commuting family of weak$^{\ast }$ continuous nonexpansive mappings"
by Slawomir Borzdynski and Andrzej Wisnicki.
Abstract: It is shown that if $S$ is a commuting family of weak$^{\ast
}$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact
convex subset $C$ of the dual Banach space $E$, then the set of common
fixed points of $S$ is a nonempty nonexpansive retract of $C$. This
partially solves a long-standing open problem in metric fixed point
theory in the case of commutative semigroups.
Archive classification: math.FA
Submitted from: awisnic at hektor.umcs.lublin.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.0359
or
http://arXiv.org/abs/1407.0359
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stephan Fackler
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 12:58:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Regularity properties of sectorial
operators: counterexamples and open problems" by Stephan Fackler.
Abstract: We give a survey on the different regularity properties of
sectorial operators on Banach spaces. We present the main results and
open questions in the theory and then concentrate on the known methods
to construct various counterexamples.
Archive classification: math.FA
Mathematics Subject Classification: 47D06 (Primary) 47A60, 35K90
(Secondary)
Remarks: 21 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/1407.1142
or
http://arXiv.org/abs/1407.1142
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kallol Paul, Puja Ghosh, and Debmalya Sain
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 13:01:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On rectangular constant in normed
linear spaces" by Kallol Paul, Puja Ghosh, and Debmalya Sain.
Abstract: We study the properties of rectangular constant $
\mu(\mathbb{X}) $ in a normed linear space $\mathbb{X}$. We prove that
$ \mu(\mathbb{X}) = 3$ iff the unit sphere contains a straight line
segment of length 2. In fact, we prove that the rectangular modulus
attains its upper bound iff the unit sphere contains a straight line
segment of length 2.
We prove that if the dimension of the space $\mathbb{X}$ is finite then
$\mu(\mathbb{X})$ is attained. We also prove that a normed linear space
is an inner product space iff we have sup$\{\frac{1+|t|}{\|y+tx\|}$:
$x,y \in S_{\mathbb{X}}$ with $x\bot_By\} \leq \sqrt{2}$ $\forall t$
satisfying $|t|\in (3-2\sqrt{2},\sqrt{2}+1)$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 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/1407.1353
or
http://arXiv.org/abs/1407.1353
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergo A. Episkoposian
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 13:02:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$L^1$- convergence of greedy
algorithm by generalized Walsh system" by Sergo A. Episkoposian.
Abstract: In this paper we consider the generalized Walsh system and
a problem $L^1- convergence$ of greedy algorithm of functions after
changing the values on small set.
Archive classification: math.FA
Mathematics Subject Classification: 42A65, 42A20
Submitted from: sergoep at ysu.am
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.1496
or
http://arXiv.org/abs/1407.1496
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miek Messerschmidt
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 13:45:24 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometric duality theory of cones
in dual pairs of vector spaces" by Miek Messerschmidt.
Abstract: This paper will generalize what may be termed the ``geometric
duality theory'' of real pre-ordered Banach spaces which relates
geometric properties of a closed cone in a real Banach space, to
geometric properties of the dual cone in the dual Banach space. We show
that geometric duality theory is not restricted to real pre-ordered
Banach spaces, as is done classically, but can naturally extended to
real Banach spaces endowed with arbitrary collections of closed cones.
We define geometric notions of normality, conormality, additivity and
coadditivity for members of dual pairs of real vector spaces as certain
possible interactions between two cones and two convex convex sets
containing zero. We show that, thus defined, these notions are dual
to each other under certain conditions, i.e., for a dual pair of real
vector spaces $(Y,Z)$, the space $Y$ is normal (additive) if and only if
its dual $Z$ is conormal (coadditive) and vice versa. These results are
set up in a manner so as to provide a framework to prove results in the
geometric duality theory of cones in real Banach spaces. As an example
of using this framework, we generalize classical duality results for
real Banach spaces pre-ordered by a single closed cone, to real Banach
spaces endowed with an arbitrary collections of closed cones.
As an application, we analyze some of the geometric properties of
naturally occurring cones in C*-algebras and their duals.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 46A20, Secondary: 46B10,
46B20, 46A40, 46B40, 46L05
Submitted from: mmesserschmidt at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.2434
or
http://arXiv.org/abs/1407.2434
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Riku Klen, Antti Rasila, and Jarno Talponen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 13:48:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On smoothness of quasihyperbolic
balls" by Riku Klen, Antti Rasila, and Jarno Talponen.
Abstract: We investigate properties of quasihyperbolic balls and
geodesics in Euclidean and Banach spaces. Our main result is that in
uniformly smooth Banach spaces a quasihyperbolic ball of a convex domain
is $C^1$-smooth. The question about the smoothness of quasihyperbolic
balls is old, originating back to the discussions of F.W. Gehring and
M. Vuorinen in 1970's. To our belief, the result is new also in the
Euclidean setting. We also address some other issues involving the
smoothness of quasihyperbolic balls.
We introduce an interesting application of quasihyperbolic metrics to
renormings of Banach spaces. To provide a useful tool for this approach
we turn our attention to the variational stability of quasihyperbolic
geodesics. Several examples and illustrations are provided.
Archive classification: math.FA math.CV
Mathematics Subject Classification: 30C65, 46T05, 46B03
Remarks: 19 pages, 4 figures
Submitted from: antti.rasila at iki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.2403
or
http://arXiv.org/abs/1407.2403
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, 21 Jul 2014 13:50:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An extension of James's compactness
theorem" by Ioannis Gasparis.
Abstract: Let X and Y be Banach spaces and F a subset of B_{Y^*}. Endow
Y with the topology \tau_F of pointwise convergence on F. Let T: X^* \to
Y be a bounded linear operator which is (w^*, \tau_F) continuous. Assume
that every vector in the range of T attains its norm at an element of
F. Then it is proved that T is (w^*,w) continuous.
Archive classification: math.FA
Mathematics Subject Classification: 46
Remarks: 15 pages
Submitted from: ioagaspa at math.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.3655
or
http://arXiv.org/abs/1407.3655
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Vladimir Kadets, Miguel Martin, Javier
Meri, and Dirk Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 13:51:45 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lipschitz slices and the Daugavet
equation for Lipschitz operators" by Vladimir Kadets, Miguel Martin,
Javier Meri, and Dirk Werner.
Abstract: We introduce a substitute for the concept of slice for the case
of non-linear Lipschitz functionals and transfer to the non-linear case
some results about the Daugavet and the alternative Daugavet equations
previously known only for linear operators.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04. Secondary 46B80,
46B22, 47A12
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.4018
or
http://arXiv.org/abs/1407.4018
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: Mon, 21 Jul 2014 13:53:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Consequences of the
Marcus/Spielman/Stivastava solution to the Kadison-Singer Problem"
by Peter G. Casazza.
Abstract: It is known that the famous, intractible 1959 Kadison-Singer
problem in $C^{*}$-algebras is equivalent to fundamental unsolved problems
in a dozen areas of research in pure mathematics, applied mathematics and
Engineering. The recent surprising solution to this problem by Marcus,
Spielman and Srivastava was a significant achievement and a significant
advance for all these areas of research.
We will look at many of the known equivalent forms of the Kadison-Singer
Problem and see what are the best new theorems available in each
area of research as a consequence of the work of Marcus, Spielman and
Srivastave. In the cases where {\it constants} are important for the
theorem, we will give the best constants available in terms of a {\it
generic constant} taken from \cite{MSS}. Thus, if better constants
eventually become available, it will be simple to adapt these new
constants to the theorems.
Archive classification: math.FA
Mathematics Subject Classification: 42A05, 42A10, 42A16, 43A50, 46B03,
46B07, 46L05,
Submitted from: casazzap at missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.4768
or
http://arXiv.org/abs/1407.4768
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kallol Paul, Debmalya Sain and Lokenath
Debnath
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Jul 2014 13:55:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A conjecture on the
characterisation of inner product spaces" by Kallol Paul, Debmalya Sain
and Lokenath Debnath.
Abstract: We study the properties of strongly orthonormal Hamel basis in
the sense of Birkhoff-James in a finite dimensional real normed linear
space that are analogous to the properties of orthonormal basis in
an inner product space. We relate the notion of strongly orthonormal
Hamel basis in the sense of Birkhoff-James with the notions of best
approximation and best coapproximation in a finite dimensional real normed
linear space. We prove that the existence of best coapproximation to any
element of the normed linear space out of any one dimensional subspace
and its coincidence with the best approximation to that element out of
that subspace characterises a real inner product space of dimension( >
2). Finally we conjecture that a finite dimensional real smooth normed
space of dimension ($>2$) is an inner product space iff given any element
on the unit sphere there exists a strongly orthonormal Hamel basis in
the sense of Birkhoff-James containing that element.
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/1407.5016
or
http://arXiv.org/abs/1407.5016
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Iian B. Smythe
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:09:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Borel equivalence relations in
the space of bounded operators" by Iian B. Smythe.
Abstract: We consider various notions of equivalence in the space
of bounded operators on a Hilbert space, including modulo finite
rank operators, modulo Schatten $p$-classes, and modulo compact
operators. Using Hjorth's theory of turbulence, the latter two are
shown to be not classifiable by countable structures, while the first
cannot be reduced to the orbit equivalence relation of any Polish group
action. The results for modulo finite rank and modulo compact operators
are also shown for the restrictions of these equivalence relations to the
space of projection operators. Families of non-classifiable equivalence
relations on sequence spaces are described and utilized in these results.
Archive classification: math.LO math.OA
Mathematics Subject Classification: Primary 03E15, 47B10, Secondary
47C15, 46A45
Remarks: 36 pages
Submitted from: ibs24 at cornell.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.5325
or
http://arXiv.org/abs/1407.5325
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ben Wallis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:11:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Constructing Banach ideals using
upper $\ell_p$-estimates" by Ben Wallis.
Abstract: Using upper $\ell_p$-estimates for normalized weakly
null sequence images, we describe a new family of operator ideals
$\mathcal{WD}_{\ell_p}^{(\infty,\xi)}$ with parameters $1\leq p\leq\infty$
and $1\leq\xi\leq\omega_1$. These classes contain the completely
continuous operators, and are distinct for all choices $1\leq p\leq\infty$
and, when $p\neq 1$, for all choices $\xi\neq\omega_1$. For the case
$\xi=1$, there exists an ideal norm $\|\cdot\|_{(p,1)}$ on the class
$\mathcal{WD}_{\ell_p}^{(\infty,1)}$ under which it forms a Banach ideal.
Archive classification: math.FA
Mathematics Subject Classification: 47L20, 46B45, 46A45, 46B25
Submitted from: wallis at math.niu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.5948
or
http://arXiv.org/abs/1407.5948
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez
and Abraham Rueda Zoca
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:12:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Octahedral norms in spaces of
operators" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham
Rueda Zoca.
Abstract: We study octahedral norms in the space of bounded linear
operators between Banach spaces. In fact, we prove that $L(X,Y)$
has octahedral norm whenever $X^*$ and $Y$ have octahedral norm. As a
consequence the space of operators $L(\ell_1 ,X)$ has octahedral norm if,
and only if, $X$ has octahedral norm. These results also allows us to
get the stability of strong diameter 2 property for projective tensor
products of Banach spaces, which is an improvement of the known results
about the size of nonempty relatively weakly open subsets in the unit
ball of the projective tensor product of Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: 16 pages
Submitted from: glopezp at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.6038
or
http://arXiv.org/abs/1407.6038
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Jimenez-Vargas, J.M. Sepulcre, and
Moises Villegas-Vallecillos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:14:53 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Biduality and density in
Lipschitz function spaces" by A. Jimenez-Vargas, J.M. Sepulcre, and
Moises Villegas-Vallecillos.
Abstract: For pointed compact metric spaces $(X,d)$, we address
the biduality problem as to when the space of Lipschitz functions
$\mathrm{Lip}_0(X,d)$ is isometrically isomorphic to the bidual of the
space of little Lipschitz functions $\mathrm{lip}_0(X,d)$, and show that
this is the case whenever the closed unit ball of $\mathrm{lip}_0(X,d)$ is
dense in the closed unit ball of $\mathrm{Lip}_0(X,d)$ with respect to the
topology of pointwise convergence. Then we apply our density criterion
to prove in an alternate way the real version of a classical result which
asserts that $\mathrm{Lip}_0(X,d^\alpha)$ is isometrically isomorphic
to $\mathrm{lip}_0(X,d^\alpha)^{**}$ for any $\alpha$ in $(0,1)$.
Archive classification: math.FA
Mathematics Subject Classification: 46E10, 46E15, 46J10
Remarks: 7 pages
Submitted from: ajimenez at ual.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.7599
or
http://arXiv.org/abs/1407.7599
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yun Sung Choi, Sun Kwang Kim, Han Ju Lee
and Miguel Martin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:16:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Banach spaces with the
approximate hyperplane series property" by Yun Sung Choi, Sun Kwang Kim,
Han Ju Lee and Miguel Martin.
Abstract: We present a sufficient condition for a Banach space to have
the approximate hyperplane series property (AHSP) which actually covers
all known examples. We use this property to get a stability result to
vector-valued spaces of integrable functions. On the other hand, the
study of a possible Bishop-Phelps-Bollob\'{a}s version of a classical
result of V. Zizler leads to a new characterization of the AHSP for dual
spaces in terms of $w^*$-continuous operators and other related results.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Remarks: 12 pages
Submitted from: hanjulee at dongguk.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.7848
or
http://arXiv.org/abs/1407.7848
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sun Kwang Kim and Han Ju Lee
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:17:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Bishop-Phelps-Bollob\'as
property for operators from $\mathcal{C}(K)$ to uniformly convex spaces"
by Sun Kwang Kim and Han Ju Lee.
Abstract: We show that the pair $(C(K),X)$ has the
Bishop-Phelps-Bolloba\'as property for operators if $K$ is a compact
Hausdorff space and $X$ is a uniformly convex space.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Citation: To apprear in J. Math. Anal. Appl. 2014
Remarks: 7 pages
Submitted from: hanjulee at dongguk.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.7872
or
http://arXiv.org/abs/1407.7872
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yanni Chen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:19:30 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lebesgue and Hardy spaces for
symmetric norms I" by Yanni Chen.
Abstract: In this paper, we define and study a class $\mathcal{R}_{c}$
of norms on $L^{\infty}\left( \mathbb{T}\right) $, called $continuous\
rotationally\ symmetric \ norms$, which properly contains the class
$\left \{ \left \Vert \cdot \right \Vert _{p}:1\leq p<\infty \right \}
.$ For $\alpha \in \mathcal{R}% _{c}$ we define $L^{\alpha}\left(
\mathbb{T}\right) $ and the Hardy space $H^{\alpha}\left(
\mathbb{T}\right) $, and we extend many of the classical results,
including the dominated convergence theorem, convolution theorems,
dual spaces, Beurling-type invariant spaces, inner-outer factorizations,
characterizing the multipliers and the closed densely-defined operators
commuting with multiplication by $z$. We also prove a duality theorem
for a version of $L^{\alpha}$ in the setting of von Neumann algebras.
Archive classification: math.OA
Submitted from: yet2 at wildcats.unh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.7920
or
http://arXiv.org/abs/1407.7920
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pavlos Motakis, Daniele Puglisi and
Despoina Zisimopoulou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:21:45 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A hierarchy of separable
commutative Calkin algebras" by Pavlos Motakis, Daniele Puglisi and
Despoina Zisimopoulou.
Abstract: For specific well founded countably branching
trees $\mathcal{T}$ we construct $\mathcal{L}_\infty$ spaces
$X_{\mathcal{T}}$. For each such tree $\mathcal{T}$ the Calkin algebra
of $X_{\mathcal{T}}$ strongly resembles $C(\mathcal{T})$, the algebra of
continuous functions defined on $\mathcal{T}$ and in the case in which
$\mathcal{T}$ has finite height, those two algebras are homomorphic. We
conclude that for every countable compact metric space $K$ with finite
Cantor-Bendixson index there exists a $\mathcal{L}_\infty$ space whose
Calkin algebra is isomorphic, as a Banach algebra, to $C(K)$.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B25, 46B28
Remarks: 28 pages
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/1407.8073
or
http://arXiv.org/abs/1407.8073
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonin Prochazka and Luis Sanchez-Gonzalez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:23:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Low distortion embeddings between
$C(K)$ spaces" by Antonin Prochazka and Luis Sanchez-Gonzalez.
Abstract: We show that, for each ordinal $\alpha<\omega_1$, the space
$C([0,\omega^\alpha])$ does not embed into $C(K)$ with distortion strictly
less than $2$ unless $K^{(\alpha)}\neq \emptyset$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B85
Remarks: 11 pages
Submitted from: antonin.prochazka at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.0211
or
http://arXiv.org/abs/1408.0211
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kevin Beanland, Daniel Freeman and Pavlos
Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:25:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The stabilized set of $p$'s in
Krivine's theorem can be disconnected" by Kevin Beanland, Daniel Freeman
and Pavlos Motakis.
Abstract: For any closed subset $F$ of $[1,\infty]$ which is either finite
or consists of the elements of an increasing sequence and its limit, a
reflexive Banach space $X$ with a 1-unconditional basis is constructed
so that in each block subspace $Y$ of $X$, $\ell_p$ is finitely block
represented in $Y$ if and only if $p \in F$. In particular, this solves
the question as to whether the stabilized Krivine set for a Banach space
had to be connected. We also prove that for every infinite dimensional
subspace $Y$ of $X$ there is a dense subset $G$ of $F$ such that the
spreading models admitted by $Y$ are exactly the $\ell_p$ for $p\in G$.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B07, 46B25, 46B45
Remarks: 25 pages
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/1408.0265
or
http://arXiv.org/abs/1408.0265
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by J. Lopez-Abad and P. Tradacete
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:27:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bases of random unconditional
convergence in Banach spaces" by J. Lopez-Abad and P. Tradacete.
Abstract: We study random unconditional convergence for a basis in
a Banach space. The connections between this notion and classical
unconditionality are explored. In particular, we analyze duality
relations, reflexivity, uniqueness of these bases and existence of
unconditional subsequences.
Archive classification: math.FA
Mathematics Subject Classification: 46B09, 46B15
Submitted from: ptradace at math.uc3m.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.0478
or
http://arXiv.org/abs/1408.0478
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by William B. Johnson, Amir Bahman Nasseri,
Gideon Schechtman and Tomasz Tkocz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 8 Aug 2014 13:28:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Injective Tauberian operators
on $L_1$ and operators with dense range on $\ell_\infty$" by William
B. Johnson, Amir Bahman Nasseri, Gideon Schechtman and Tomasz Tkocz.
Abstract: There exist injective Tauberian operators on $L_1(0,1)$ that
have dense, non closed range. This gives injective, non surjective
operators on $\ell_\infty$ that have dense range. Consequently, there
are two quasi-complementary, non complementary subspaces of $\ell_\infty$
that are isometric to $\ell_\infty$.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B08, 47A53
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/1408.1443
or
http://arXiv.org/abs/1408.1443
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by M. G. Cabrera-Padilla, J. A.
Chavez-Dominguez, A. Jimenez-Vargas, and Moises Villegas-Vallecillos
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:05:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lipschitz tensor product" by
M. G. Cabrera-Padilla, J. A. Chavez-Dominguez, A. Jimenez-Vargas, and
Moises Villegas-Vallecillos.
Abstract: Inspired by ideas of R. Schatten in his celebrated monograph
on a theory of cross-spaces, we introduce the notion of a Lipschitz
tensor product X\boxtimes E of a pointed metric space and a Banach space
E as a certain linear subspace of the algebraic dual of Lipo(X,E^*). We
prove that <Lipo(X,E^*),X\boxtimes E> forms a dual pair. We prove that
X\boxtimes E is linearly isomorphic to the linear space of all finite-rank
continuous linear operators from (X^#,T) into E, where X^# denotes the
space Lipo(X,K) and T is the topology of pointwise convergence of X^#. The
concept of Lipschitz tensor product of elements of X^# and E^* yields the
space X^#\boxast E^* as a certain linear subspace of the algebraic dual
of X\boxtimes E. To ensure the good behavior of a norm on X\boxtimes E
with respect to the Lipschitz tensor product of Lipschitz functionals
(mappings) and bounded linear functionals (operators), the concept of
dualizable (respectively, uniform) Lipschitz cross-norm on X\boxtimes
E is defined. We show that the Lipschitz injective norm epsilon,
the Lipschitz projective norm pi and the Lipschitz p-nuclear norm d_p
(1<=p<=infty) are uniform dualizable Lipschitz cross-norms on X\boxtimes
E. In fact, epsilon is the least dualizable Lipschitz cross-norm and
pi is the greatest Lipschitz cross-norm on X\boxtimes E. Moreover,
dualizable Lipschitz cross-norms alpha on X\boxtimes E are characterized
by satisfying the relation epsilon<=alpha<=pi. In addition, the Lipschitz
injective (projective) norm on X\boxtimes E can be identified with the
injective (respectively, projective) tensor norm on the Banach-space
tensor product between the Lipschitz-free space over X and E. In terms
of the space X^#\boxast E^*, we describe the spaces of Lipschitz compact
(finite-rank, approximable) operators from X to E^$.
Archive classification: math.FA
Mathematics Subject Classification: 26A16, 46B28, 46E15, 47L20
Remarks: 31 pages
Submitted from: ajimenez at ual.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.1874
or
http://arXiv.org/abs/1408.1874
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Enrique A. Sanchez-Perez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:07:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The product duality formula in
Banach space theory" by Enrique A. Sanchez-Perez.
Abstract: In this paper we analyze a definition of product of Banach
spaces that is naturally associated by duality with an abstract notion
of space of multiplication operators. This dual relation allows to
understand several constructions coming from different fields of the
functional analysis, that can be seen as instances of the abstract one
when a particular product is considered. Some relevant examples and
applications are shown.
Archive classification: math.FA
Mathematics Subject Classification: 46A32, 46E30, 47A30, 46B10
Remarks: 14 pages
Submitted from: easancpe at mat.upv.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.2147
or
http://arXiv.org/abs/1408.2147
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Thomas Schlumprecht
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:09:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On Zippin's embedding theorem of
Banach spaces into Banach spaces with bases" by Thomas Schlumprecht.
Abstract: We present a new proof of Zippin's Embedding Theorem, that
every separable reflexive Banach space embeds into one with shrinking
and boundedly complete basis, and every Banach space with a separable
dual embeds into one with a shrinking basis. This new proof leads to
improved versions of other embedding results.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Submitted from: schlump at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.3311
or
http://arXiv.org/abs/1408.3311
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Amit Maji and P. D. Srivastava
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:17:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On some geometric properties of
generalized Musielak-Orlicz sequence space and corresponding operator
ideals" by Amit Maji and P. D. Srivastava.
Abstract: Let $\bold{\Phi}=(\phi_n)$ be a Musielak-Orlicz function, $X$
be a real Banach space and $A$ be any infinite matrix. In this paper,
a generalized vector-valued Musielak-Orlicz sequence space $l_{\bold
{\Phi}}^{A}(X)$ is introduced. It is shown that the space is complete
normed linear space under certain conditions on the matrix $A$. It
is also shown that $l_{\bold{\Phi}}^{A}(X)$ is a $\sigma$- Dedikind
complete whenever $X$ is so. We have discussed some geometric properties,
namely, uniformly monotone, uniform Opial property for this space. Using
the sequence of $s$-number (in the sense of Pietsch), the operators
of $s$-type $l_{\bold{\Phi}}^{A}$ and operator ideals under certain
conditions on the matrix $A$ are discussed.
Archive classification: math.FA
Mathematics Subject Classification: 46A45, 47B06, 47L20
Remarks: 18 pages
Submitted from: amaji at maths.iitkgp.ernet.in
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.3528
or
http://arXiv.org/abs/1408.3528
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eusebio Gardella and Martino Lupini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:19:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Representations of \'{e}tale
groupoids on $L^p$-spaces" by Eusebio Gardella and Martino Lupini.
Abstract: For $p\in (1,\infty)$, we study representations of \'{e}tale
groupoids on $L^{p}$-spaces. Our main result is a generalization of
Renault's disintegration theorem for representations of \'{e}tale
groupoids on Hilbert spaces. We establish a correspondence
between $L^{p}$-representations of an \'{e}tale groupoid $G$,
contractive $L^{p}$-representations of $C_{c}(G)$, and tight regular
$L^{p}$-representations of any countable inverse semigroup of open
slices of $G$ that is a basis for the topology of $G$. We define analogs
$F^{p}(G)$ and $F_{\mathrm{red}}^{p}(G)$ of the full and reduced groupoid
C*-algebras using representations on $L^{p}$-spaces. As a consequence
of our main result, we deduce that every contractive representation
of $F^{p}(G)$ or $F_{\mathrm{red}}^{p}(G)$ is automatically completely
contractive. Examples of our construction include the following natural
families of Banach algebras: discrete group $L^{p}$-operator algebras,
the analogs of Cuntz algebras on $L^{p}$-spaces, and the analogs of
AF-algebras on $L^{p} $-spaces. Our results yield new information
about these objects: their matricially normed structure is uniquely
determined. More generally, groupoid $L^{p}$-operator algebras
provide analogs of several families of classical C*-algebras, such as
Cuntz-Krieger C*-algebras, tiling C*-algebras, and graph C*-algebras.
Archive classification: math.OA
Mathematics Subject Classification: 47L10, 22A22 (Primary) 46H05
(Secondary)
Remarks: 52 pages
Submitted from: mlupini at yorku.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.3752
or
http://arXiv.org/abs/1408.3752
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by H. Garth Dales
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:21:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Maximal ideals in commutative
Banach algebras" by H. Garth Dales.
Abstract: We show that each maximal ideal in a commutative Banach algebra
has codimension 1.
Archive classification: math.FA math.RA
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/1408.3815
or
http://arXiv.org/abs/1408.3815
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Adam W. Marcus, Daniel A. Spielman, and
Nikhil Srivastava,
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:23:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Ramanujan graphs and the solution
of the Kadison-Singer problem" by Adam W. Marcus, Daniel A. Spielman,
and Nikhil Srivastava,.
Abstract: We survey the techniques used in our recent resolution of
the Kadison-Singer problem and proof of existence of Ramanujan Graphs
of every degree: mixed characteristic polynomials and the method
of interlacing families of polynomials. To demonstrate the method of
interlacing families of polynomials, we give a simple proof of Bourgain
and Tzafriri's restricted invertibility principle in the isotropic case.
Archive classification: math.SP math.CO math.OA
Mathematics Subject Classification: 05C50, 46L05, 26C10
Remarks: A version of this paper will appear in the proceedings of
the 2014
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.4421
or
http://arXiv.org/abs/1408.4421
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yong Jiao, Anming Yang, Lian Wu, and Rui Yi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:27:04 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The predual and John-Nirenberg
inequalities on generalized BMO martingale spaces" by Yong Jiao, Anming
Yang, Lian Wu, and Rui Yi.
Abstract: In this paper we introduce the generalized BMO martingale
spaces by stopping time sequences, which enable us to characterize the
dual spaces of martingale Hardy-Lorentz spaces $H_{p,q}^s$ for $0<p\leq1,
1<q<\infty$. Moreover, by duality we obtain a John-Nirenberg theorem
for the generalized BMO martingale spaces when the stochastic basis
is regular. We also extend the boundedness of fractional integrals to
martingale Hardy-Lorentz spaces.
Archive classification: math.FA
Mathematics Subject Classification: 60G46, 60G42
Remarks: 23pages
Submitted from: jiaoyong at csu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.4641
or
http://arXiv.org/abs/1408.4641
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dario Trevisan
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:28:22 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A short proof of Stein's universal
multiplier theorem" by Dario Trevisan.
Abstract: We give a short proof of Stein's universal multiplier theorem,
purely by probabilistic methods, thus avoiding any use of harmonic
analysis techniques (complex interpolation or transference methods).
Archive classification: math.FA
Submitted from: dario.trevisan at sns.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.4752
or
http://arXiv.org/abs/1408.4752
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kevin Beanland, Ryan Causey, and Pavlos
Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 22 Aug 2014 10:30:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Arbitrarily distortable Banach
spaces of higher order" by Kevin Beanland, Ryan Causey, and Pavlos
Motakis.
Abstract: We study an ordinal rank on the class of Banach spaces with
bases that quantifies the distortion of the norm of a given Banach
space. The rank $AD(\cdot)$, introduced by P. Dodos, uses the transfinite
Schreier familes and has the property that $AD(X) < \omega_1$ if and
only if $X$ is arbitrarily distortable. We prove several properties
of this rank as well as some new results concerning higher order
$\ell_1$ spreading models. We also compute this rank for for several
Banach spaces. In particular, it is shown that class of Banach spaces
$\mathfrak{X}^{\omega^\xi}_{0,1}$ , which each admit $\ell_1$ and $c_0$
spreading models hereditarily, and were introduced by S.A. Argyros, the
first and third author, satisfy $AD(\mathfrak{X}^{\omega^\xi}_{0,1}) =
\omega^\xi + 1$. This answers some questions of Dodos.
Archive classification: math.FA
Submitted from: CAUSEYRM at mailbox.sc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.5065
or
http://arXiv.org/abs/1408.5065
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Assaf Naor and Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 12:56:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Metric ${X}_p$ inequalities"
by Assaf Naor and Gideon Schechtman.
Abstract: We show that if $m,n\in \mathbb{N}$ and $k\in \{1,\ldots,
n\}$ satisfy $m\ge \frac{n^{3/2}}{\sqrt{k}}$ then for every
$p\in [2,\infty)$ and $f:\mathbb{Z}_{4m}^n\to \mathbb{R}$ we have
\begin{equation} \frac{1}{\binom{n}{k}}\sum_{\substack{S\subseteq
\{1,\ldots,n\}\\|S|= k}}\frac{\mathbb{E}\left[\big|f\big(x+2m\sum_{j\in
S} \varepsilon_j e_j\big)-f(x)\big|^p\right]}{m^p}\lesssim_p
\frac{k}{n}\sum_{j=1}^n\mathbb{E}\big[\left|
f(x+e_j)-f(x)\right|^p\big]+\left(\frac{k}{n}\right)^{\frac{p}{2}}
\mathbb{E}\big[\left|f\left(x+ \varepsilon{e}\right)-f(x)\right|^p\big],
\end{equation} where the expectation is with respect to
$(x,\varepsilon)\in \mathbb{Z}_{4m}^n\times \{-1,1\}^n$ chosen
uniformly at random and $e_1,\ldots e_n$ is the standard basis of
$\mathbb{Z}_{4m}^n$. The above inequality is a nonlinear extension of
a linear inequality for Rademacher sums that was proved by Johnson,
Maurey, Schechtman and Tzafriri in 1979. We show that for the above
statement to hold true it is necessary that $m$ tends to infinity with
$n$. The formulation (and proof) of the above inequality completes
the long-standing search for bi-Lipschitz invariants that serve as an
obstruction to the nonembeddability of $L_p$ spaces into each other,
the previously understood cases of which were metric notions of type and
cotype, which fail to certify the nonembeddability of $L_q$ into $L_p$
when $2<q<p$. Among the consequences of the above inequality are new
quantitative restrictions on the bi-Lipschitz embeddability into $L_p$
of snowflakes of $L_q$ and integer grids in $\ell_q^n$, for $2<q<p$. As a
byproduct of our investigations, we also obtain results on the geometry
of the Schatten $p$ trace class $S_p$ that are new even in the linear
setting.
Archive classification: math.FA math.MG math.OA
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/1408.5819
or
http://arXiv.org/abs/1408.5819
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Afonso S. Bandeira and Ramon van Handel
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 12:57:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sharp nonasymptotic bounds on the
norm of random matrices with independent entries" by Afonso S. Bandeira
and Ramon van Handel.
Abstract: We obtain nonasymptotic bounds on the spectral norm of
random matrices with independent entries that improve significantly
on earlier results. If $X$ is the $n\times n$ symmetric matrix with
$X_{ij}\sim N(0,b_{ij}^2)$, we show that $$\mathbf{E}\|X\|\lesssim
\max_i\sqrt{\sum_{j}b_{ij}^2} +\max_{ij}|b_{ij}|\sqrt{\log n}. $$ This
bound is optimal in the sense that a matching lower bound holds under mild
assumptions, and the constants are sufficiently sharp that we can often
capture the precise edge of the spectrum. Analogous results are obtained
for rectangular matrices and for more general subgaussian or heavy-tailed
distributions of the entries, and we derive tail bounds in addition to
bounds on the expected norm. The proofs are based on a combination of
the moment method and geometric functional analysis techniques. As an
application, we show that our bounds immediately yield the correct phase
transition behavior of the spectral edge of random band matrices and of
sparse Wigner matrices. We also recover a result of Seginer on the norm
of Rademacher matrices.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60B20, 46B09, 60F10
Remarks: 23 pages
Submitted from: rvan at princeton.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.6185
or
http://arXiv.org/abs/1408.6185
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. J. Dilworth, Denka Kutzarova, and N.
Lovasoa Randrianarivony
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 12:59:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The transfer of property $(\beta)$
of Rolewicz by a uniform quotient" by S. J. Dilworth, Denka Kutzarova,
and N. Lovasoa Randrianarivony.
Abstract: We provide a Laakso construction to prove that the property
of having an equivalent norm with the property $(\beta)$ of Rolewicz
is qualitatively preserved via surjective uniform quotient mappings
between separable Banach spaces. On the other hand, we show that the
$(\beta)$-modulus is not quantitatively preserved via such a map by
exhibiting two uniformly homeomorphic Banach spaces that do not have
$(\beta)$-moduli of the same power-type even under renorming.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B20 (Primary), 46B80, 46T99, 51F99
(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/1408.6424
or
http://arXiv.org/abs/1408.6424
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Carlos H. Jimenez and Ignacio Villanueva
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 13:01:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Characterization of dual mixed
volumes via polymeasures" by Carlos H. Jimenez and Ignacio Villanueva.
Abstract: We prove a characterization of the dual mixed volume in terms
of functional properties of the polynomial associated to it. To do
this, we use tools from the theory of multilinear operators on spaces of
continuos functions. Along the way we reprove, with these same techniques,
a recently found characterization of the dual mixed volume.
Archive classification: math.FA
Submitted from: ignaciov at mat.ucm.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.6796
or
http://arXiv.org/abs/1408.6796
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by I. Asekritova, N. Kruglyak and M. Mastylo
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 13:02:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Interpolation of Fredholm
operators" by I. Asekritova, N. Kruglyak and M. Mastylo.
Abstract: We prove novel results on interpolation of Fredholm operators
including an abstract factorization theorem. The main result of this
paper provides sufficient conditions on the parameters $\theta \in (0,1)$
and $q\in \lbrack 1,\infty ]$ under which an operator $A$ is a Fredholm
operator from the real interpolation space $(X_{0},X_{1})_{\theta
,q}$ to $(Y_{0},Y_{1})_{\theta ,q} $ for a given operator $A\colon
(X_{0},X_{1})\rightarrow (Y_{0},Y_{1})$ between compatible pairs of Banach
spaces such that its restrictions to the endpoint spaces are Fredholm
operators. These conditions are expressed in terms of the corresponding
indices generated by the $K$-functional of elements from the kernel of the
operator $A$ in the interpolation sum $X_{0}+X_{1}$. If in addition $q\in
\lbrack 1,\infty )$ and $A$ is invertible operator on endpoint spaces,
then these conditions are also necessary. We apply these results to
obtain and present an affirmative solution of the famous Lions-Magenes
problem on the real interpolation of closed subspaces. We also discuss
some applications to the spectral theory of operators as well as to
perturbation of the Hardy operator by identity on weighted $L_{p}$-spaces.
Archive classification: math.FA
Submitted from: mastylo at amu.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1408.7024
or
http://arXiv.org/abs/1408.7024
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Olav Nygaard
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 13:04:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uniform boundedness deciding sets,
and a problem of M. Valdivia" by Olav Nygaard.
Abstract: We prove that if a set $B$ in a Banach space $X$ can be
written as an increasing, countable union $B=\cup_n B_n$ of sets $B_n$
such that no $B_n$ is uniform boundedness deciding, then also $B$ is not
uniform boundedness deciding. From this we can give a positive answer
to a question of M. Valdivia.
Archive classification: math.FA
Remarks: 5 pages
Submitted from: olav.nygaard at uia.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.0102
or
http://arXiv.org/abs/1409.0102
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Valentin Ferenczi and Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 13:06:22 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Non-unitarisable representations
and maximal symmetry" by Valentin Ferenczi and Christian Rosendal.
Abstract: We investigate questions of maximal symmetry in Banach spaces
and the structure of certain bounded non-unitarisable groups on Hilbert
space. In particular, we provide structural information about bounded
groups with an essentially unique invariant complemented subspace. This is
subsequently combined with rigidity results for the unitary representation
of ${\rm Aut}(T)$ on $\ell_2(T)$, where $T$ is the countably infinite
regular tree, to describe the possible bounded subgroups of ${\rm
GL}(\mathcal H)$ extending a well-known non-unitarisable representation
of $\mathbb F_\infty$.
As a related result, we also show that a transitive norm on a separable
Banach space must be strictly convex.
Archive classification: 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/1409.0141
or
http://arXiv.org/abs/1409.0141
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Oleg Reinov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 13:11:24 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "O-frames for operators in Banach
spaces" by Oleg Reinov.
Abstract: These notes are formal. Here, in this abstract, not in the
note, we should say that all that is in the text was done, essentially,
by Aleksander Pe{\l}czy\'nski. BUT: Anyhow, a new notion of an O-frame
for an operator is introduced. For the operators in separable spaces,
it is shown that a operator has an O-frame iff it has the BAP iff it
can be factored through a Banach space with a basis. Applications are
given. However, looking around, I'd say that, e.g., a notion of a Banach
frame (and also O-frame) was implicitely introduced by great Aleksander
Pe{\l}czy\'nski.
Archive classification: math.FA
Mathematics Subject Classification: 46B28
Remarks: 11 pages, was as a SPb Math. Soc. preprint, in RUSSIAN!
Submitted from: orein51 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.0165
or
http://arXiv.org/abs/1409.0165
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S Dutta and D Khurana
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 13:14:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Ordinal indices of small subspaces
of $L_p$" by S Dutta and D Khurana.
Abstract: We calculate ordinal $L_p$ index defined in "An ordinal L_p
index for Banach spaces with an application to complemented subspaces
of L_p" authored by J. Bourgain, H. P. Rosenthal and G. Schechtman,
for Rosenthal's space $X_p$, $\ell_p$ and $\ell_2$. We show a subspace
of $L_p$ $(2 < p < \infty)$ non isomorphic to $\ell_2$ embeds in
$\ell_p$ if and only if its ordinal index is minimum possible. We
also give a sufficient condition for a $\mathcal{L}_p$ subspace of
$\ell_p\oplus\ell_2$ to be isomorphic to $X_p$.
Archive classification: math.FA
Submitted from: divyakhurana11 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.2330
or
http://arXiv.org/abs/1409.2330
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dong Hoon Cho and Yun Sung Choi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 14:34:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bishop-Phelps-Bolloba's theorem
on bounded closed convex sets" by Dong Hoon Cho and Yun Sung Choi.
Abstract: This paper deals with the \emph{Bishop-Phelps-Bollob\'as
property} (\emph{BPBp} for short) on bounded closed convex subsets of a
Banach space $X$, not just on its closed unit ball $B_X$. We firstly prove
that the \emph{BPBp} holds for bounded linear functionals on arbitrary
bounded closed convex subsets of a real Banach space. We show that for
all finite dimensional Banach spaces $X$ and $Y$ the pair $(X,Y)$ has the
\emph{BPBp} on every bounded closed convex subset $D$ of $X$, and also
that for a Banach space $Y$ with property $(\beta )$ the pair $(X,Y)$
has the \emph{BPBp} on every bounded closed absolutely convex subset $D$
of an arbitrary Banach space $X$. For a bounded closed absorbing convex
subset $D$ of $X$ with positive modulus convexity we get that the pair
$(X,Y)$ has the \emph{BPBp} on $D$ for every Banach space $Y$. We further
obtain that for an Asplund space $X$ and for a locally compact Hausdorff
$L$, the pair $(X, C_0(L))$ has the \emph{BPBp} on every bounded closed
absolutely convex subset $D$ of $X$. Finally we study the stability of
the \emph{BPBp} on a bounded closed convex set for the $\ell_1$-sum or
$\ell_{\infty}$-sum of a family of Banach spaces.
Archive classification: math.FA
Submitted from: meimi200 at postech.ac.kr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.3008
or
http://arXiv.org/abs/1409.3008
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Thomas Schlumprecht and Andras Zsak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 12 Sep 2014 14:35:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The algebra of bounded linear
operators on $\ell_p\oplus\ell_q$ has infinitely many closed ideals"
by Thomas Schlumprecht and Andras Zsak.
Abstract: We prove that in the reflexive range $1<p<q<\infty$ the algebra
of all bounded linear operators on $\ell_p\oplus\ell_q$ has infinitely
many closed ideals. This solves a problem raised by A. Pietsch in his book
`Operator ideals'.
Archive classification: math.FA
Mathematics Subject Classification: 47L20, 46B25
Remarks: 18 pages
Submitted from: a.zsak at dpmms.cam.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.3480
or
http://arXiv.org/abs/1409.3480
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dimosthenis Drivaliaris and Nikos
Yannakakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Sep 2014 12:48:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The angle of an operator and
range and kernel complementarity" by Dimosthenis Drivaliaris and Nikos
Yannakakis.
Abstract: We show that if the angle of a bounded linear operator on a
Banach space with closed range is less than $\pi$, then its range and
kernel are complementary. We also show that in finite dimensions and
up to rotations this simple geometric property characterizes operators
for which range and kernel are complementary. For operators on a Hilbert
space we present a sufficient condition, involving the distance of the
boundary of the numerical range from the origin, for the range and the
kernel to be complementary.
Archive classification: math.FA
Mathematics Subject Classification: 47A05, 47A12, 47A10, 47B44, 46B20
Submitted from: d.drivaliaris at fme.aegean.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.4195
or
http://arXiv.org/abs/1409.4195
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fernanda Botelho
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Sep 2014 12:50:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isometries and Hermitian operators
on Zygmund spaces" by Fernanda Botelho.
Abstract: In this paper we characterize the isometries of subspaces of
the little Zygmund space. We show that the isometries of these spaces
are surjective and represented as integral operators. We also show that
all hermitian operators on these settings are bounded.
Archive classification: math.FA
Mathematics Subject Classification: 46E15, 47B15, 47B38
Submitted from: mbotelho at memphis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.5378
or
http://arXiv.org/abs/1409.5378
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Fernanda Botelho and James Jamison
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Sep 2014 12:52:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isometries and Hermitian operators
on $\mathcal{B}_0(\triangle, E)$" by Fernanda Botelho and James Jamison.
Abstract: In this paper we describe the surjective linear isometries on a
vector valued little Bloch space with range space a strictly convex and
smooth complex Banach space. We also describe the hermitian operators
and the generalized bi-circular projections supported by these spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46E15, 47B15, 47B38
Submitted from: mbotelho at memphis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.5381
or
http://arXiv.org/abs/1409.5381
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kati Ain and Eve Oja
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Sep 2014 12:57:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On $(p,r)$-null sequences and
their relatives" by Kati Ain and Eve Oja.
Abstract: Let $1\leq p < \infty$ and $1\leq r \leq p^\ast$, where $p^\ast$
is the conjugate index of $p$. We prove an omnibus theorem, which provides
numerous equivalences for a sequence $(x_n)$ in a Banach space $X$ to
be a $(p,r)$-null sequence. One of them is that $(x_n)$ is $(p,r)$-null
if and only if $(x_n)$ is null and relatively $(p,r)$-compact. This
equivalence is known in the ''limit'' case when $r=p^\ast$, the case of
the $p$-null sequence and $p$-compactness. Our approach is more direct
and easier than those applied for the proof of the latter result. We
apply it also to characterize the unconditional and weak versions of
$(p,r)$-null sequences.
Archive classification: math.FA
Submitted from: kati.ain at ut.ee
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.6476
or
http://arXiv.org/abs/1409.6476
Return-path: <alspach at math.okstate.edu>
Subject: Announcement of a special issue of Annals of Functional Analysis
From: Dale Alspach <alspach at math.okstate.edu>
Date: Sun, Oct 12, 2014 at 3:56 PM
To: banach at mathdept.okstate.edu
Dear Colleague,
I would like to inform you that a special issue (2016) of the Annals
of Functional Analysis (AFA) is dedicated to Professor Anthony To-Ming
Lau for his significant contributions to several areas of Functional
Analysis, Abstract Harmonic Analysis and Operator Theory.
The journal particularly invites articles related to works of A.
T.-M. Lau, but other papers within the scope of the journal (MSC43,
MSC46 and MSC47) are warmly welcomed. The usual reviewing procedures
and standards of AFA will be applied to all papers for the special
issue. Preliminary papers or summaries of results previously published
are not acceptable.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Submission should be done via the online submission of AFA at:
http://www.emis.de/journals/AFA/
The deadline for submission is: *** 30 March 2015 ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Please let the editor-in-chief know whether you are potentially able
to have a contribution to this issue or not (and give an approximate
date for receiving your paper, if possible).
Best wishes,
M. S. Moslehian
Editor-in-chief
http://www.um.ac.ir/~moslehian/
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Niels Jakob Laustsen and Richard Skillicorn
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:38:27 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Splittings of extensions of the
algebra of bounded operators on a space" by Niels Jakob Laustsen and
Richard Skillicorn.
Abstract: We show that there exist a Banach space E, a unital Banach
algebra A with Jacobson radical rad A, and a continuous, surjective
algebra homomorphism f from A onto the Banach algebra B(E) of bounded
operators on E such that ker f = rad A and the corresponding extension
{0} -> rad A -> A -> B(E) -> {0} is singular (in the sense that rad A
has trivial multiplication) and splits algebraically, but it does not
split strongly. This conclusion complements the work of Bade, Dales, and
Lykova (Mem. Amer. Math. Soc. 1999). The Banach space E that we use is
a quotient of the l_2-direct sum of an infinite sequence of James-type
quasi-reflexive Banach spaces; it was originally introduced by Read
(J. London Math. Soc. 1989).
Archive classification: math.FA
Submitted from: r.skillicorn at lancaster.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.8203
or
http://arXiv.org/abs/1409.8203
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Demuth, Franz Hanauska, Marcel
Hansmann, and Guy Katriel
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:40:22 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Estimating the number of
eigenvalues of linear operators on Banach spaces" by Michael Demuth,
Franz Hanauska, Marcel Hansmann, and Guy Katriel.
Abstract: Let $L_0$ be a bounded operator on a Banach space, and consider
a perturbation $L=L_0+K$, where $K$ is compact. This work is concerned
with obtaining bounds on the number of eigenvalues of $L$ in subsets
of the complement of the essential spectrum of $L_0$, in terms of
the approximation numbers of the perturbing operator $K$. Our results
can be considered as wide generalizations of classical results on the
distribution of eigenvalues of compact operators, which correspond to the
case $L_0=0$. They also extend previous results on operators in Hilbert
space. Our method employs complex analysis and a new finite-dimensional
reduction, allowing us to avoid using the existing theory of determinants
in Banach spaces, which would require strong restrictions on $K$. Several
open questions regarding the sharpness of our results are raised,
and an example is constructed showing that there are some essential
differences in the possible distribution of eigenvalues of operators in
general Banach spaces, compared to the Hilbert space case.
Archive classification: math.SP math.FA
Submitted from: marcel.hansmann at mathematik.tu-chemnitz.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.8569
or
http://arXiv.org/abs/1409.8569
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mark Rudelson
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:42:18 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "On the complexity of the set of
unconditional convex bodies" by Mark Rudelson.
Abstract: We show that for any t>1, the set of unconditional convex bodies
in R^n contains a t-separated subset of cardinality at least 0.1 exp exp
(C(t) n). This implies that there exists an unconditional convex body in
R^n which cannot be approximated within the distance d by a projection
of a polytope with N faces unless N > exp(c(d)n). We also show that
for t>2, the cardinality of a t-separated set of completely symmetric
bodies in R^n does not exceed exp exp (c(t)(log n)^2).
Archive classification: math.MG math.FA
Remarks: 17 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/1410.0092
or
http://arXiv.org/abs/1410.0092
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sun Kwang Kim, Han Ju Lee, and Miguel
Martin
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:43:59 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Bishop-Phelps-Bollob\'as property
for bilinear forms on spaces of continuous functions" by Sun Kwang Kim,
Han Ju Lee, and Miguel Martin.
Abstract: It is shown that the Bishop-Phelps-Bollob\'as theorem holds
for bilinear forms on the complex $C_0(L_1)\times C_0(L_2)$ for arbitrary
locally compact topological Hausdorff spaces $L_1$ and $L_2$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.0514
or
http://arXiv.org/abs/1410.0514
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jochen Gl\"uck
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:46:19 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Spectral and asymptotic properties
of contractive semigroups on non-Hilbert spaces" by Jochen Gl\"uck.
Abstract: We analyse $C_0$-semigroups of contractive operators on
real-valued $L^p$-spaces for $p \not= 2$ and on other classes of
non-Hilbert spaces. We show that, under some regularity assumptions on
the semigroup, the geometry of the unit ball of those spaces forces
the semigroup's generator to have only trivial (point) spectrum
on the imaginary axis. This has interesting consequences for the
asymptotic behaviour as $t \to \infty$. For example, we can show that
a contractive and eventually norm continuous $C_0$-semigroup on a
real-valued $L^p$-space automatically converges strongly if $p \not\in
\{1,2,\infty\}$.
Archive classification: math.FA
Mathematics Subject Classification: 47D06
Remarks: 26 pages
Submitted from: jochen.glueck at uni-ulm.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.2502
or
http://arXiv.org/abs/1410.2502
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez, Bernardo Gonzalez,
C. Hugo Jimenez, and Rafael Villa
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:48:31 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Rogers-Shephard inequality for
log-concave functions" by David Alonso-Gutierrez, Bernardo Gonzalez,
C. Hugo Jimenez, and Rafael Villa.
Abstract: In this paper we prove different functional inequalities
extending the classical Rogers-Shephard inequalities for convex
bodies. The original inequalities provide an optimal relation between the
volume of a convex body and the volume of several symmetrizations of the
body, such as, its difference body. We characterize the equality cases
in all these inequalities. Our method is based on the extension of the
notion of a convolution body of two convex sets to any pair of log-concave
functions and the study of some geometrical properties of these new sets.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary 52A20, Secondary 39B62, 46N10
Remarks: 24 pages
Submitted from: carloshugo at us.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.2556
or
http://arXiv.org/abs/1410.2556
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Martino Lupini
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:50:10 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Uniqueness, universality, and
homogeneity of the noncommutative Gurarij space" by Martino Lupini.
Abstract: We realize the noncommutative Gurarij space $\mathbb{NG}$
defined by Oikhberg as the Fra\"{\i}ss\'{e} limit of the class of
finite-dimensional $1$-exact operator spaces. As a consequence we deduce
that the noncommutative Gurarij space is unique up to completely isometric
isomorphism, homogeneous, and universal among separable $1$-exact operator
spaces. Moreover we show that $\mathbb{NG}$ is isometrically isomorphic
to the Gurarij Banach space. Therefore $\mathbb{NG}$ can be thought as
a canonical operator space structure on the Gurarij Banach space.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 46L07 (Primary) 03C30 (Secondary)
Remarks: 24 pages
Submitted from: mlupini at yorku.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.3345
or
http://arXiv.org/abs/1410.3345
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez
and Abraham Rueda
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:52:29 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Subspaces of Banach spaces with big
slices" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda.
Abstract: We study when diameter two properties pass down to subspaces. We
obtain that the slice two property (respectively diameter two property,
strong diameter two property) passes down from a Banach space $X$ to
a subspace $Y$ whenever $Y$ is complemented by a norm one projection
with finite-dimensional kernel (respectively the quotient $X/Y$ is
finite dimensional, $X/Y$ is strongly regular). Also we study the same
problem for dual properties of the above ones, as having octahedral,
weakly octahedral or 2-rough norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: 12 pages
Submitted from: glopezp at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4324
or
http://arXiv.org/abs/1410.4324
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Becerra Guerrero, Gines Lopez-Perez
and Abraham Rueda
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:55:30 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Diameter two properties in James
spaces" by Julio Becerra Guerrero, Gines Lopez-Perez and Abraham Rueda.
Abstract: We study the diameter two properties in the spaces $JH$,
$JT_\infty$ and $JH_\infty$. We show that the topological dual space of
the previous Banach spaces fails every diameter two property. However,
we prove that $JH$ and $JH_{\infty}$ satisfy the strong diameter two
property, and so the dual norm of these spaces is octahedral. Also we find
a closed hyperplane $M$ of $JH_\infty$ whose topological dual space enjoys
the $w^*$-strong diameter two property and also $M$ and $M^*$ have an
octahedral norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: 19 pages
Submitted from: glopezp at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4325
or
http://arXiv.org/abs/1410.4325
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Cwikel and Richard Rochberg
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:56:56 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Nigel Kalton and complex
interpolation of compact operators" by Michael Cwikel and Richard
Rochberg.
Abstract: This is the fourth of a series of papers surveying some small
part of the remarkable work of our friend and colleague Nigel Kalton. We
have written it as part of a tribute to his memory. It does not contain
new results. This time we discuss Nigel's partial solutions (obtained
jointly with one of us) of the problem of whether the complex method
of interpolation preserves the compactness of operators. This problem
is now 51 years old and still lacks a complete solution. We also survey
some other partial solutions of this problem, obtained before and after
the above mentioned joint work. We plan a technical sequel to this paper,
which may contain some small new results and will probably conclude this
series devoted to Nigel's research.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B70
Remarks: 12 pages
Submitted from: mcwikel at math.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4527
or
http://arXiv.org/abs/1410.4527
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Delgado, Michael Ruzhansky and
Baoxiang Wang
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 13:58:41 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Approximation property and
nuclearity on mixed-norm $L^p$, modulation and Wiener amalgam spaces"
by Julio Delgado, Michael Ruzhansky and Baoxiang Wang.
Abstract: In this paper we first prove the metric approximation
property for weighted mixed-norm Lebesgue spaces. Then, using Gabor
frame representation we show that the same property holds in weighted
modulation and Wiener amalgam spaces. As a consequence, Grothendieck's
theory becomes applicable, and we give criteria for nuclearity and
r-nuclearity for operators acting on these space as well as derive the
corresponding trace formulae. Finally, we apply the notion of nuclearity
to functions of the harmonic oscillator on modulation spaces.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary 46B26, 47B38, Secondary 47G10,
47B06, 42B35
Remarks: 20 pages
Submitted from: m.ruzhansky at imperial.ac.uk
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4687
or
http://arXiv.org/abs/1410.4687
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Julio Flores, Jordi Lopez-Abad, and Pedro
Tradacete
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 14:00:34 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Banach lattice versions of strict
singularity" by Julio Flores, Jordi Lopez-Abad, and Pedro Tradacete.
Abstract: We explore the relation between lattice versions of strict
singularity for operators from a Banach lattice to a Banach space. In
particular, we study when the class of disjointly strictly singular
operators, those not invertible on the span of any disjoint sequence,
coincides with that of lattice strictly singular operators, i.e. those not
invertible on any (infinite dimensional) sublattice. New results are given
which help to clarify the existing relation between these two classes.
Archive classification: math.FA
Mathematics Subject Classification: 46B42, 47B60
Submitted from: ptradace at math.uc3m.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4752
or
http://arXiv.org/abs/1410.4752
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jarno Talponen
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 21 Oct 2014 14:01:57 -0500
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Note on order-isomorphic isometric
embeddings of some recent function spaces" by Jarno Talponen.
Abstract: We investigate certain recently introduced ODE-determined
varying exponent $L^p$ spaces. It turns out that these spaces are
finitely representable in a concrete universal varying exponent
$\ell^p$ space. Moreover, this can be accomplished in a natural unified
fashion. This leads to order-isomorphic isometric embeddings of all of
the above $L^p$ spaces to an ultrapower of the above varying exponent
$\ell^p$ space.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 46E30, 46B08, 46B04, 46B42, 46B45,
34-XX
Submitted from: talponen at iki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.4961
or
http://arXiv.org/abs/1410.4961
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M. F. Castillo, Valentin Ferenczi and
Manuel Gonzalez
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 12 Nov 2014 14:52:24 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Singular twisted sums generated
by complex interpolation" by Jesus M. F. Castillo, Valentin Ferenczi
and Manuel Gonzalez.
Abstract: We present new methods to obtain singular twisted sums
$X\oplus_\Omega X$ (i.e., exact sequences $0\to X\to X\oplus_\Omega X \to
X\to 0$ in which the quotient map is strictly singular), in which $X$
is the interpolation space arising from a complex interpolation scheme
and $\Omega$ is the induced centralizer.
Although our methods are quite general, in our applications we
are mainly concerned with the choice of $X$ as either a Hilbert space,
or Ferenczi's uniformly convex Hereditarily Indecomposable space. In
the first case, we construct new singular twisted Hilbert spaces,
including the only known example so far: the Kalton-Peck space $Z_2$. In
the second case we obtain the first example of an H.I. twisted sum of
an H.I. space. We then use Rochberg's description of iterated twisted
sums to show that there is a sequence $\mathcal F_n$ of H.I. spaces
so that $\mathcal F_{m+n}$ is a singular twisted sum of $\mathcal F_m$
and $\mathcal F_n$, while for $l>n$ the direct sum $\mathcal F_n \oplus
\mathcal F_{l+m}$ is a nontrivial twisted sum of $\mathcal F_l$ and
$\mathcal F_{m+n}$.
We also introduce and study the notion of disjoint singular twisted
sum of K\"othe function spaces and construct several examples involving
reflexive $p$-convex K\"othe function spaces, which include the function
version of the Kalton-Peck space $Z_2$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B70, 46M18
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.5505
or
http://arXiv.org/abs/1410.5505
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mario Chica, Vladimir Kadets, Miguel
Martin, Javier Meri, and Soloviova
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 12 Nov 2014 14:53:57 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Two refinements of the
Bishop-Phelps-Bollob\'as modulus" by Mario Chica, Vladimir Kadets,
Miguel Martin, Javier Meri, and Soloviova.
Abstract: Extending the celebrated result by Bishop and Phelps that the
set of norm attaining functionals is always dense in the topological
dual of a Banach space, Bollob\'as proved the nowadays known as the
Bishop-Phelps-Bollob\'as theorem, which allows to approximate at the same
time a functional and a vector in which it almost attains the norm. Very
recently, two Bishop-Phelps-Bollob\'as moduli of a Banach space have been
introduced [J. Math. Anal. Appl. 412 (2014), 697--719] to measure, for
a given Banach space, what is the best possible Bishop-Phelps-Bollob\'as
theorem in this space. In this paper we present two refinements of the
results of that paper. On the one hand, we get a sharp general estimation
of the Bishop-Phelps-Bollob\'as modulus as a function of the norms of
the point and the functional, and we also calculate it in some examples,
including Hilbert spaces. On the other hand, we relate the modulus
of uniform non-squareness with the Bishop-Phelps-Bollob\'as modulus
obtaining, in particular, a simpler and quantitative proof of the fact
that a uniformly non-square Banach space cannot have the maximum value
of the Bishop-Phelps-Bollob\'as modulus.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Submitted from: mmartins at ugr.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.5570
or
http://arXiv.org/abs/1410.5570
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Silvia Lassalle and Pablo Turco
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 12 Nov 2014 14:55:34 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "The weak bounded approximation
property for $\mathcal A$" by Silvia Lassalle and Pablo Turco.
Abstract: Fixed a Banach operator ideal $\mathcal A$, we introduce and
investigate the weak bounded approximation property for $\mathcal A$,
which is strictly weaker than the bounded approximation property for
$\mathcal A$ of Lima, Lima and Oja (2010). We relate the weak BAP for
$\mathcal A$ with approximation properties given by tensor norms and show
that the metric approximation property of order $p$ of Saphar is the
weak BAP for the ideal of $p'$-summing operators, $1<p<\infty$, $\frac
1p + \frac 1{p'}=1$. Under this framework, we address the question of
approximation properties passing from $X'$ to $X$ or from $X''$ to $X'$.
Archive classification: math.FA
Mathematics Subject Classification: 47B10, 46A32, 46B28
Remarks: 15 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/1410.5670
or
http://arXiv.org/abs/1410.5670
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pandelis Dodos, Vassilis Kanellopoulos and
Konstantinos Tyros
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 12 Nov 2014 15:16:52 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "A concentration inequality
for product spaces" by Pandelis Dodos, Vassilis Kanellopoulos and
Konstantinos Tyros.
Abstract: We prove a concentration inequality which asserts that, under
some mild regularity conditions, every random variable defined on the
product of sufficiently many probability spaces exhibits pseudorandom
behavior.
Archive classification: math.PR math.CO math.FA
Remarks: 11 pages, no figures
Submitted from: pdodos at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.5965
or
http://arXiv.org/abs/1410.5965
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pandelis Dodos, Vassilis Kanellopoulos and
Thodoris Karageorgos
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 12 Nov 2014 15:18:22 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Szemer\'{e}di's regularity lemma
via martingales" by Pandelis Dodos, Vassilis Kanellopoulos and Thodoris
Karageorgos.
Abstract: We prove a variant of the abstract probabilistic version of
Szemer\'{e}di's regularity lemma, due to Tao, which applies to a number
of structures (including graphs, hypergraphs, hypercubes, graphons, and
many more) and works for random variables in $L_p$ for any $p>1$. Our
approach is based on martingale difference sequences.
Archive classification: math.CO math.FA math.PR
Remarks: 24 pages, no figures
Submitted from: pdodos at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.5966
or
http://arXiv.org/abs/1410.5966
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gerard Buskes and Chris Schwanke
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 12 Nov 2014 15:20:30 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Functional completions of
archimedean vector lattices" by Gerard Buskes and Chris Schwanke.
Abstract: We study completions of Archimedean vector lattices relative to
any nonempty set of positively-homogeneous functions on finite-dimensional
real vector spaces. Examples of such completions include square mean
closed and geometric closed vector lattices, amongst others. These
functional completions also lead to a universal definition of the
complexification of any Archimedean vector lattice and a theory of tensor
products and powers of complex vector lattices in a companion paper.
Archive classification: math.FA
Mathematics Subject Classification: 06F20, 46A40
Submitted from: mmbuskes at olemiss.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.5878
or
http://arXiv.org/abs/1410.5878
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Afonso S. Bandeira, Dustin G. Mixon, and
Joel Moreira
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 12:40:31 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "A conditional construction of
restricted isometries" by Afonso S. Bandeira, Dustin G. Mixon, and
Joel Moreira.
Abstract: We study the restricted isometry property of a matrix
that is built from the discrete Fourier transform matrix by collecting
rows indexed by quadratic residues. We find an $\epsilon>0$ such that,
conditioned on a folklore conjecture in number theory, this matrix
satisfies the restricted isometry property with sparsity parameter
$K=\Omega(M^{1/2+\epsilon})$, where $M$ is the number of rows.
Archive classification: math.FA cs.IT math.IT math.NT
Remarks: 6 pages
Submitted from: moreira at math.ohio-state.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.6457
or
http://arXiv.org/abs/1410.6457
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by E. Casini, E. Miglierina, and L. Piasecki
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 12:44:13 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Hyperplanes in the space
of convergent sequences and preduals of $\ell_1$" by E. Casini,
E. Miglierina, and L. Piasecki.
Abstract: The main aim of the present paper is to investigate various
structural properties of hyperplanes of $c$, the Banach space of the
convergent sequences. In particular, we give an explicit formula for the
projection constants and we prove that an hyperplane of $c$ is isometric
to the whole space if and only if it is $1$-complemented. Moreover,
we obtain the classification of those hyperplanes for which their duals
are isometric to $\ell_{1}$ and we give a complete description of the
preduals of $\ell_{1}$ under the assumption that the standard basis of
$\ell_{1}$ is weak$^{*}$-convergent.
Archive classification: math.FA
Mathematics Subject Classification: 46B45 (Primary), 46B04 (Secondary)
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/1410.7801
or
http://arXiv.org/abs/1410.7801
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Richard Lechner and Paul F.X. Mueller
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 12:47:52 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Localization and projections on
bi--parameter BMO" by Richard Lechner and Paul F.X. Mueller.
Abstract: We prove that for any operator T on bi--parameter BMO the
identity factors through T or Id - T. As a consequence, bi--parameter
BMO is a primary Banach space. Bourgain's localization method provides
the conceptual framework of our proof. It consists in replacing the
factorization problem on the non--separable Banach space bi--parameter BMO
by its localized, finite dimensional counterpart. We solve the resulting
finite dimensional factorization problems by combinatorics of colored
dyadic rectangles.
Archive classification: math.FA
Mathematics Subject Classification: 46B25, 60G46, 46B07, 46B26, 30H35
Submitted from: Richard.Lechner at jku.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1410.8786
or
http://arXiv.org/abs/1410.8786
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Cwikel and Richard Rochberg
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 14:22:39 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Lecture notes on complex
interpolation of compactness" by Michael Cwikel and Richard Rochberg.
Abstract:
Suppose that the linear operator $T$ maps $X_0$ compactly to $Y_0$
and also maps $X_1$ boundedly to $Y_1$. We deal once again with the
51 year old question of whether $T$ also always maps the complex
interpolation space $[X_0,X_1]_\theta$ compactly to $[Y_0,Y_1]_\theta$.
This is a short preliminary version of our promised technical sequel
to our earlier paper arXiv:1410.4527 on this topic.
It contains the following two small new partial results: (i) The answer
to the above question is yes, in the particular case where $Y_0$ is
a UMD-space.
(ii) The answer to the above question is yes for given spaces $X_0$,
$X_1$, $Y_0$ and $Y_1$ if the answer to the "dualized" or
"adjoint" version of the question for the duals of these
particular spaces is yes.
In fact we deduce (i) from (ii) and from an earlier result obtained
jointly by one of us with Nigel Kalton.
It is remarked that a proof of a natural converse of (ii) would
answer the general form of this question completely.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B70, 46B50. Secondary 46E15
Remarks: 7 pages
Submitted from: mcwikel at math.technion.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.0171
or
http://arXiv.org/abs/1411.0171
This is an announcement for the paper "An improvement of a theorem of
Heinrich, Mankiewicz, Sims, and Yost" by Trond A. Abrahamsen.
Abstract: Heinrich, Mankiewicz, Sims, and Yost proved that every
separable subspace of a Banach space Y is contained in a separable ideal
in Y. We improve this result by replacing the term "ideal" with the term
"almost isometric ideal". As a consequence of this we obtain, in terms
of subspaces, characterizations of diameter 2 properties, the Daugavet
property along with the properties of being an almost square space and
an octahedral space.
Archive classification: math.FA
Mathematics Subject Classification: 46B20 (Primary) 46B07 (Secondary)
Remarks: 13 pages
Submitted from: trond.a.abrahamsen at uia.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.0425
or
http://arXiv.org/abs/1411.0425
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Azagra and Carlos Mudarra
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 14:51:22 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Global approximation of convex
functions by differentiable convex functions on Banach spaces" by Daniel
Azagra and Carlos Mudarra.
Abstract:
We show that if $X$ is a Banach space whose dual $X^{*}$ has an
equivalent locally uniformly rotund (LUR) norm, then for every open convex
$U\subseteq X$, for every $\varepsilon >0$, and for every continuous and
convex function $f:U \rightarrow \mathbb{R}$ (not necessarily bounded on
bounded sets) there exists a convex function $g:X \rightarrow \mathbb{R}$
of class $C^1(U)$ such that $f-\varepsilon\leq g\leq f$ on $U.$ We
also show how the problem of global approximation of continuous (not
necessarily bounded on bounded sets) and convex functions by $C^k$ smooth
convex functions can be reduced to the problem of global approximation
of Lipschitz convex functions by $C^k$ smooth convex functions.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 52A99, 26B25, 41A30
Remarks: 8 pages
Submitted from: dazagra at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.0471
or
http://arXiv.org/abs/1411.0471
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Nigel Kalton and Lutz Weis
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 14:53:25 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "The $H^{\infty}$--functional
calculus and square function estimates" by Nigel Kalton and Lutz Weis.
Abstract:
Using notions from the geometry of Banach spaces we introduce square
functions $\gamma(\Omega,X)$ for functions with values in an arbitrary
Banach space $X$. We show that they have very convenient function space
properties comparable to the Bochner norm of $L_2(\Omega,H)$ for a Hilbert
space $H$. In particular all bounded operators $T$ on $H$ can be extended
to $\gamma(\Omega,X)$ for all Banach spaces $X$. Our main applications
are characterizations of the $H^{\infty}$--calculus that extend known
results for $L_p$--spaces from \cite{CowlingDoustMcIntoshYagi}. With these
square function estimates we show, e.~g., that a $c_0$--group of operators
$T_s$ on a Banach space with finite cotype has an $H^{\infty}$--calculus
on a strip if and only if $e^{-a|s|}T_s$ is $R$--bounded for some $a >
0$. Similarly, a sectorial operator $A$ has an $H^{\infty}$--calculus on
a sector if and only if $A$ has $R$--bounded imaginary powers. We also
consider vector valued Paley--Littlewood $g$--functions on $UMD$--spaces.
Archive classification: math.FA
Submitted from: Lutz.weis at kit.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.0472
or
http://arXiv.org/abs/1411.0472
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino and Joedson Santos
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 14:56:00 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Lineability and uniformly dominated
sets of summing nonlinear" by Daniel Pellegrino and Joedson Santos.
Abstract:
In this note we prove an abstract version of a result from 2002 due to
Delgado and Pi\~{n}ero on absolutely summing operators. Several
applications are presented; some of them in the multilinear framework and
some in a completely nonlinear setting. In a final section we investigate
the size of the set of non uniformly dominated sets of linear operators
under the point of view of lineability.
Archive classification: math.FA
Submitted from: pellegrino at pq.cnpq.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.1100
or
http://arXiv.org/abs/1411.1100
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Debmalya Sain, Kallol Paul and Kanhaiya Jha
From: Dale Alspach <alspach at math.okstate.edu>
Date: Fri, 14 Nov 2014 14:58:12 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Strictly convex space : Strong
orthogonality and conjugate diameters" by Debmalya Sain, Kallol Paul
and Kanhaiya Jha.
Abstract:
In a normed linear space X an element x is said to be orthogonal
to another element y in the sense of Birkhoff-James, written as $ x
\perp_{B}y, $ iff $ \| x \| \leq \| x + \lambda y \| $ for all scalars $
\lambda.$ We prove that a normed linear space X is strictly convex iff
for any two elements x, y of the unit sphere $ S_X$, $ x \perp_{B}y $
implies $ \| x + \lambda y \| > 1~ \forall~ \lambda \neq 0. $ We apply
this result to find a necessary and sufficient condition for a Hamel basis
to be a strongly orthonormal Hamel basis in the sense of Birkhoff-James
in a finite dimensional real strictly convex space X. Applying the result
we give an estimation for lower bounds of $ \| tx+(1-t)y\|, t \in [0,1]
$ and $ \| y + \lambda x \|, ~\forall ~\lambda $ for all elements $
x,y \in S_X $ with $ x \perp_B y. $ We find a necessary and sufficient
condition for the existence of conjugate diameters through the points $
e_1,e_2 \in ~S_X $ in a real strictly convex space of dimension 2. The
concept of generalized conjuagte diameters is then developed for a real
strictly convex smooth space of finite dimension.
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/1411.1464
or
http://arXiv.org/abs/1411.1464
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daher Mohammad
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:42:50 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "K(X,Y) as subspace complemented
of L(X,Y)" by Daher Mohammad.
Abstract:
Let X,Y be two Banach spaces ; in the first part of this work, we show
that K(X,Y) contains a complemented copy of c0 if Y contains a copy
of c0 and each bounded sequence in Y has a subsequece which is w*
convergente. Afterward we obtain some results of M.Feder and G.Emmanuele:
Finally in this part we study the relation between the existence of
projection from L(X,Y) on K(X,Y) and the existence of pro- jection from
K(X,Y ) on K(X,Y) if Y has the approximation property. In the second
part we study the Radon-Nikodym property in L(X,Y):
Archive classification: math.FA
Mathematics Subject Classification: 46EXX
Remarks: 21 pages
Submitted from: m.daher at orange.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.2217
or
http://arXiv.org/abs/1411.2217
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Kasper Green Larsen and Jelani Nelson
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:47:10 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "The Johnson-Lindenstrauss lemma
is optimal for linear dimensionality reduction" by Kasper Green Larsen
and Jelani Nelson.
Abstract:
For any $n>1$ and $0<\varepsilon<1/2$, we show the existence of an
$n^{O(1)}$-point subset $X$ of $\mathbb{R}^n$ such that any linear map
from $(X,\ell_2)$ to $\ell_2^m$ with distortion at most $1+\varepsilon$
must have $m = \Omega(\min\{n, \varepsilon^{-2}\log n\})$. Our lower
bound matches the upper bounds provided by the identity matrix and the
Johnson-Lindenstrauss lemma, improving the previous lower bound of Alon
by a $\log(1/\varepsilon)$ factor.
Archive classification: cs.IT cs.CG cs.DS math.FA math.IT
Submitted from: minilek at seas.harvard.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.2404
or
http://arXiv.org/abs/1411.2404
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Cuth and Michal Doucha
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:48:53 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Lipschitz-free spaces over
ultrametric spaces" by Marek Cuth and Michal Doucha.
Abstract:
We prove that the Lipschitz-free space over a separable ultrametric
space has a monotone Schauder basis and is isomorphic to $\ell_1$. This
extends results of A. Dalet using an alternative approach.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B15, 54E35
Submitted from: marek.cuth at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.2434
or
http://arXiv.org/abs/1411.2434
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:51:21 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Metric characterizations of some
classes of Banach spaces" by Mikhail I. Ostrovskii.
Abstract:
The main purpose of the paper is to present some recent results
on metric characterizations of superreflexivity and the Radon-Nikod\'ym
property.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary 46B85, Secondary: 05C12,
20F67, 30L05, 46B07, 46B22
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.3366
or
http://arXiv.org/abs/1411.3366
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tengiz Kopaliani, Nino Samashvili and
Shalva Zviadadze
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:52:45 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "On the upper and lower estimates
of norms in variable exponent spaces" by Tengiz Kopaliani, Nino Samashvili
and Shalva Zviadadze.
Abstract:
In the present paper we investigate some geometrical properties of the
norms in Banach function spaces. Particularly there is shown
that if exponent $1/p(\cdot)$ belongs to $BLO^{1/\log}$
then for the norm of corresponding variable exponent
Lebesgue space we have the following lower estimate $$\left\|\sum
\chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}\leq
C\|f\|_{p(\cdot)}$$ where $\{Q\}$ defines disjoint partition
of $[0;1]$. Also we have constructed variable exponent
Lebesgue space with above property which does not possess
following upper estimation $$\|f\|_{p(\cdot)}\leq C\left\|\sum
\chi_{Q}\|f\chi_{Q}\|_{p(\cdot)}/\|\chi_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}.
$$
Archive classification: math.FA
Mathematics Subject Classification: 42B35, 42B20, 46B45, 42B25
Remarks: 13 pages
Submitted from: sh.zviadadze at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.3461
or
http://arXiv.org/abs/1411.3461
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Florent Pierre Baudier
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:54:20 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "On the $(\beta)$-distortion of
countably branching hyperbolic trees" by Florent Pierre Baudier.
Abstract:
In this note we show that the distortion incurred by a bi-Lipschitz
embedding of the countably branching hyperbolic tree of height $N$ into
a Banach space admitting a norm satisfying Rolewicz property $(\beta)$
with power type $p>1$ is at least of the order of $\log(N)^{1/p}$. An
application of our result gives a quantitative version of the
non-embeddability of countably branching hyperbolic trees into reflexive
Banach spaces admitting an equivalent asymptotically uniformly smooth
norm and an equivalent asymptotically uniformly convex norm from Baudier,
Kalton and Lancien.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B20, 46B85
Remarks: 5 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/1411.3915
or
http://arXiv.org/abs/1411.3915
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jorge Tomas Rodriguez
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:56:16 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "On the norm of products of
polynomials on ultraproduct of Banach spaces" by Jorge Tomas Rodriguez.
Abstract:
The purpose of this article is to study the problem of finding sharp
lower bounds for the norm of the product of polynomials in the
ultraproducts of Banach spaces $(X_i)_{\mathfrak U}$. We show that, under
certain hypotheses, there is a strong relation between this problem and
the same problem for the spaces $X_i$.
Archive classification: math.FA
Submitted from: jtrodrig at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.5894
or
http://arXiv.org/abs/1411.5894
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kobos
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 26 Nov 2014 14:58:07 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Hyperplanes of finite-dimensional
normed spaces with the maximal relative projection constant" by
Tomasz Kobos.
Abstract:
The \emph{relative projection constant} $\lambda(Y, X)$ of normed spaces
$Y \subset X$ is defined as $\lambda(Y, X) = \inf \{ ||P|| : P \in
\mathcal{P}(X, Y) \}$, where $\mathcal{P}(X, Y)$ denotes the set of
all continuous projections from $X$ onto $Y$. By the well-known result
of Bohnenblust for every $n$-dimensional normed space $X$ and its
subspace $Y$ of codimension $1$ the inequality $\lambda(Y, X) \leq 2 -
\frac{2}{n}$ holds. The main goal of the paper is to study the equality
case in the theorem of Bohnenblust. We establish an equivalent condition
for the equality $\lambda(Y, X) = 2 - \frac{2}{n}$ and present several
applications. We prove that every three-dimensional space has a subspace
with the projection constant less than $\frac{4}{3} - 0.0007$. This
gives a non-trivial upper bound in the problem posed by Bosznay and
Garay. In the general case, we give an upper bound for the number
of $(n-1)$-dimensional subspaces with the maximal relative projection
constant in terms of the facets of the unit ball of $X$. As a consequence,
every $n$-dimensional normed space $X$ has an $(n-1)$-dimensional
subspace $Y$ with $\lambda(Y, X) < 2-\frac{2}{n}$. This contrasts with
the seperable case in which it is possible that every hyperplane has a
maximal possible projection constant.
Archive classification: math.FA
Mathematics Subject Classification: Primary 41A35, 41A65, 47A30, 52A21
Remarks: 15 pages
Submitted from: tkobos at wp.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.6214
or
http://arXiv.org/abs/1411.6214
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gideon Schechtman
From: Dale Alspach <alspach at math.okstate.edu>
Date: Thu, 27 Nov 2014 19:48:41 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Three observations regarding
Schatten p classes" by Gideon Schechtman.
Abstract:
The paper contains three results, the common feature of which is
that they deal with the Schatten $p$ class. The first is a presentation of
a new complemented subspace of $C_p$ in the reflexive range (and $p\not=
2$). This construction answers a question of Arazy and Lindestrauss from
1975. The second result relates to tight embeddings of finite dimensional
subspaces of $C_p$ in $C_p^n$ with small $n$ and shows that $\ell_p^k$
nicely embeds into $C_p^n$ only if $n$ is at least proportional to $k$
(and then of course the dimension of $C_p^n$ is at least of order
$k^2$). The third result concerns single element of $C_p^n$ and shows
that for $p>2$ any $n\times n$ matrix of $C_p$ norm one and zero diagonal
admits, for every $\varepsilon>0$, a $k$-paving of $C_p$ norm at most
$\varepsilon$ with $k$ depending on $\varepsilon$ and $p$ only.
Archive classification: math.FA
Mathematics Subject Classification: 47B10, 46B20, 46B28
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/1411.4427
or
http://arXiv.org/abs/1411.4427
_______________________________________________
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Banach at mathdept.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Relations Between Banach Space Theory and Geometric Measure Theory workshop,
08 - 12 June 2015, University of Warwick, UK
From: Olga Maleva <O.Maleva at bham.ac.uk>
Date: Thu, 27 Nov 2014 15:48:36 +0000
To: "Banach at mathdept.okstate.edu" <Banach at mathdept.okstate.edu>
1st ANNOUNCEMENT OF THE WORKSHOP
Relations Between Banach Space Theory and Geometric Measure Theory
08 - 12 June 2015
University of Warwick
United Kingdom
Plenary speakers include:
Jesus M F Castillo (Universidad de Extremadura)
Gilles Godefroy (Universit<E9> Paris VI)
William B Johnson (Texas A&M University)
Assaf Naor* (Princeton University)
Mikhail Ostrovskii (St.-John's University)
Gideon Schechtman (Weizmann Institute)
Thomas Schlumprecht (Texas A&M University)
*To be confirmed
The homepage of the workshop is: http://tinyurl.com/BanachGMT
To register please follow the links on the homepage of the workshop.
For further information on the workshop please contact the organisers:
* David Preiss <d dot preiss at warwick dot ac dot uk>
* Olga Maleva <o dot maleva at bham dot ac dot uk>
We expect to be able to cover some expenses for a number of participants.
Please read more information on the homepage about the funding.
We ask to register your attendance at the workshop by 15 April 2015.
The Workshop is supported by a European Research Council grant.
_______________________________________________
Banach mailing list
Banach at mathdept.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Address Changes
From: Dale Alspach <alspach at math.okstate.edu>
Date: Mon, 15 Dec 2014 16:19:48 -0600
To: <banach at mathdept.okstate.edu>
The Banach list is changing its address. Messages should be sent to
banach at mathdept.okstate.edu.
The list location for subscribing or unsubscribing is now
https://www.mathdept.okstate.edu/cgi-bin/mailman/listinfo/banach
The URL for lists of past postings and other information is
https://math.okstate.edu/people/alspach/banach/index.html
My current address alspach at math.okstate.edu should continue to work
but banach at math.okstate.edu will stop working sometime in the next few
weeks.
Best Wishes for the New Year,
Dale Alspach
_______________________________________________
Banach mailing list
Banach at mathdept.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Address Changes
From: Dale Alspach <alspach at math.okstate.edu>
Date: Mon, 15 Dec 2014 16:19:48 -0600
To: <banach at mathdept.okstate.edu>
The Banach list is changing its address. Messages should be sent to
banach at mathdept.okstate.edu.
The list location for subscribing or unsubscribing is now
https://www.mathdept.okstate.edu/cgi-bin/mailman/listinfo/banach
The URL for lists of past postings and other information is
https://math.okstate.edu/people/alspach/banach/index.html
My current address alspach at math.okstate.edu should continue to work
but banach at math.okstate.edu will stop working sometime in the next few
weeks.
Best Wishes for the New Year,
Dale Alspach
_______________________________________________
Banach mailing list
Banach at mathdept.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Banach J. Math Anal and Ann. Funct. Anal.
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 10:44:37 -0600
To: <banach at mathdept.okstate.edu>
Duke University Press partners with the Tusi Mathematical Research Group
to publish the Annals of Functional Analysis (AFA) and the Banach
Journal of Mathematical Analysis (BJMA). In 2015, Duke University Press
will begin publishing both journals.
AFA, started in 2010, and BJMA, started in 2007, are online-only
journals included in the prestigious "Reference List Journals" covered
by MathSciNet and indexed by Zentralblatt Math, Scopus and Thomson
Reuters (ISI).
With the start of their 2015 volumes under the guidance of strong
editorial boards, the journals will increase in frequency from two to
four issues per year. The journals publish research papers and critical
survey articles that focus on, but are not limited to, functional
analysis, abstract harmonic analysis and operator theory. AFA and BJMA
have rapidly established themselves as providing high-level scholarship
that addresses important questions in the study of mathematical
analysis. The journals are no longer open access but papers will be
freely available in Project Euclid 5 years after publication.
As before, they will be available on Project Euclid at
http://projecteuclid.org/euclid.bjma [1] and
http://projecteuclid.org/euclid.afa [2]
Editor-in-chief
M. S. Moslehian
===========================================================
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Subject: Abstract of a paper by Aleksandar Nikolov
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 10:50:09 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Randomized rounding for the
largest $j$-simplex problem" by Aleksandar Nikolov.
Abstract:
The maximum volume $j$-simplex problem asks to compute the
$j$-dimensional simplex of maximum volume inside the convex hull of
a given set of $n$ points in $\mathbb{R}^d$. We give a deterministic
approximation algorithm for this problem which achieves an approximation
ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathsf{NP}$-hard
to approximate within a factor of $2^{cj}$ for some constant $c$. Our
algorithm also approximates the problem of finding the largest determinant
principal $j\times j$ submatrix of a rank $d$ positive semidefinite
matrix, with approximation ratio $e^{j + o(j)}$. We achieve our
approximation by rounding solutions to a generlization of the $D$-optimal
design problem, or, equivalently, the dual of an appropriate smallest
enclosing ellipsoid probelm. Our arguments give a short and simple proof
of a restricted invertibility principle for determinants.
Archive classification: cs.CG cs.DS math.FA
Submitted from: anikolov at cs.rutgers.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.0036
or
http://arXiv.org/abs/1412.0036
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Astrid Berg, Lukas Parapatits, Franz E.
Schuster, and Manuel Weberndorfer
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 10:52:32 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Log-concavity properties of
Minkowski valuations" by Astrid Berg, Lukas Parapatits, Franz E. Schuster,
and Manuel Weberndorfer.
Abstract:
New Orlicz Brunn-Minkowski inequalities are established for rigid
motion compatible Minkowski valuations of arbitrary degree. These extend
classical log-concavity properties of intrinsic volumes and generalize
seminal results of Lutwak and others. Two different approaches which
refine previously employed techniques are explored. It is shown that
both lead to the same class of Minkowski valuations for which these
inequalities hold. An appendix by Semyon Alesker contains the proof of
a new classification of generalized translation invariant valuations.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A38, 52B45
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/1411.7891
or
http://arXiv.org/abs/1411.7891
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier and Eric Ricard
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 10:54:03 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "The non-commutative Khintchine
inequalities for $0<p<1$" by Gilles Pisier and Eric Ricard.
Abstract:
We give a proof of the Khintchine inequalities in non-commutative
$L_p$-spaces for all $0< p<1$. These new inequalities are valid for the
Rademacher functions or Gaussian random variables, but also for more
general sequences, e.g. for the analogues of such random variables in
free probability. We also prove a factorization for operators from
a Hilbert space to a non commutative $L_p$-space, which is new for
$0<p<1$. We end by showing that Mazur maps are H\"older on semifinite
von Neumann algebras.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 2000 MSC 46L51, 46L07, 47L25, 47L20
Submitted from: pisier at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.0222
or
http://arXiv.org/abs/1412.0222
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jarno Talponen
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 10:55:29 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Uniform-to-proper duality of
geometric properties of Banach spaces and their ultrapowers" by Jarno
Talponen.
Abstract:
In this note various geometric properties of a Banach space $X$ are
characterized by means of weaker corresponding geometric properties
involving an ultrapower $X^\mathcal{U}$. The characterizations do not
depend on the particular choice of the free ultrafilter $\mathcal{U}$. For
example, a point $x\in S_X$ is an MLUR point if and only if $j(x)$
(given by the canonical inclusion $j\colon X \to X^\mathcal{U}$) in
$\B_{X^\mathcal{U}}$ is an extreme point; a point $x\in S_X$ is LUR if
and only if $j(x)$ is not contained in any non-degenerate line segment
of $S_{X^\mathcal{U}}$; a Banach space $X$ is URED if and only if there
are no $x,y \in S_{X^\mathcal{U}}$, $x\neq y$, with $x-y \in j(X)$.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 03H05, 46B20, 46M07, 46B10
Submitted from: talponen at iki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.1279
or
http://arXiv.org/abs/1412.1279
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Megrelishvili
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 10:58:12 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "A note on dependence of families
having bounded variation" by Michael Megrelishvili.
Abstract:
We show that for arbitrary linearly ordered set $X$ any bounded
family of real valued functions on $X$ with bounded total variation
does not contain independent subsequences. As a corollary we generalize
Helly's sequential compactness theorem.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 54F15, 54D30, 06A05
Remarks: 7 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/1412.1515
or
http://arXiv.org/abs/1412.1515
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Gabriyelyan, J. Kcakol, W. Kubis, and W.
Marciszewski
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 11:00:44 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Networks for the weak topology
of Banach and Frechet spaces" by S. Gabriyelyan, J. Kcakol, W. Kubis,
and W. Marciszewski.
Abstract:
We start the systematic study of Fr\'{e}chet spaces which are
$\aleph$-spaces in the weak topology. A topological space $X$ is an
$\aleph_0$-space or an $\aleph$-space if $X$ has a countable $k$-network
or a $\sigma$-locally finite $k$-network, respectively. We are motivated
by the following result of Corson (1966): If the space $C_{c}(X)$
of continuous real-valued functions on a Tychonoff space $X$ endowed
with the compact-open topology is a Banach space, then $C_{c}(X)$
endowed with the weak topology is an $\aleph_0$-space if and only if
$X$ is countable. We extend Corson's result as follows: If the space
$E:=C_{c}(X)$ is a Fr\'echet lcs, then $E$ endowed with its weak topology
$\sigma(E,E')$ is an $\aleph$-space if and only if $(E,\sigma(E,E'))$
is an $\aleph_0$-space if and only if $X$ is countable. We obtain a
necessary and some sufficient conditions on a Fr\'echet lcs to be an
$\aleph$-space in the weak topology. We prove that a reflexive Fr\'echet
lcs $E$ in the weak topology $\sigma(E,E')$ is an $\aleph$-space if
and only if $(E,\sigma(E,E'))$ is an $\aleph_0$-space if and only if
$E$ is separable. We show however that the nonseparable Banach space
$\ell_{1}(\mathbb{R})$ with the weak topology is an $\aleph$-space.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46A03, 54H11, Secondary
22A05, 54C35
Remarks: 18 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/1412.1748
or
http://arXiv.org/abs/1412.1748
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by N. Albuquerque, G. Araujo, and D. Pellegrino
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 11:02:33 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "H\"{o}lder's inequality: some
recent and unexpected applications" by N. Albuquerque, G. Araujo, and
D. Pellegrino.
Abstract:
H\"{o}lder's inequality, since its appearance in 1888, has played a
fundamental role in Mathematical Analysis and it is, without any
doubt, one of the milestones in Mathematics. It may seem strange
that, nowadays, it keeps resurfacing and bringing new insights to the
mathematical community. In this expository article we show how a variant
of H\"{o}lder's inequality (although well-known in PDEs) was essentially
overlooked in Functional Analysis and has had a crucial (and in some
sense unexpected) influence in very recent and major breakthroughs
in Mathematics. Some of these recent advances appeared in 2012-2014
and include the theory of Dirichlet series, the famous Bohr radius
problem, certain classical inequalities (such as Bohnenblust--Hille or
Hardy--Littlewood), or even Mathematical Physics.
Archive classification: math.FA
Submitted from: pellegrino at pq.cnpq.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.2017
or
http://arXiv.org/abs/1412.2017
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tomasz Kania
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 11:04:08 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "On C*-algebras which cannot
be decomposed into tensor products with factors infinite-dimensional"
by Tomasz Kania.
Abstract:
We prove that C*-algebras which satisfy a Banach-space property of
being a Grothendieck space cannot be decomposed into a tensor product
of two infinite-dimensional Banach spaces. By a result of Pfitzner, this
class contains all von Neumann algebras and their norm-quotients. We thus
strengthen a recent result of Ghasemi who established a similar conclusion
for C*-tensor products in the case of SAW*-algebras. In particular, we
solve in the negative a problem of Simon Wassermann concerning tensorial
decompositions of the Calkin algebra in the category of Banach spaces.
Archive classification: math.OA math.FA
Submitted from: tomasz.marcin.kania at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.3621
or
http://arXiv.org/abs/1412.3621
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eusebio Gardella and Hannes Thiel
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 16 Dec 2014 11:05:35 -0600
To: <alspach at math.okstate.edu>, <banach at math.okstate.edu>
This is an announcement for the paper "Quotients of Banach algebras
acting on $L^p$-spaces" by Eusebio Gardella and Hannes Thiel.
Abstract:
We show that the class of Banach algebras that can be isometrically
represented on an $L^p$-space, for $p\neq 2$, is not closed under
quotients. This answers a question asked by Le Merdy 20 years ago. Our
methods are heavily reliant on our earlier study of Banach algebras
generated by invertible isometries of $L^p$-spaces.
Archive classification: math.OA math.FA
Mathematics Subject Classification: Primary: 47L10, 43A15. Secondary:
46J10
Remarks: 7 pages
Submitted from: gardella at uoregon.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.3985
or
http://arXiv.org/abs/1412.3985
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Peide Liu and Maofa Wang
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 30 Dec 2014 17:29:18 -0600
To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>
This is an announcement for the paper "Burkholder-Gundy-Davis inequality
in martingale Hardy spaces with variable exponent" by Peide Liu and
Maofa Wang.
Abstract:
In this paper, the classical Dellacherie's theorem about stochastic
process is extended to variable exponent Lebesgue spaces. As its
applications, we obtain variable exponent analogues of several famous
inequalities in classical martingale theory, including convexity lemma,
Burkholder-Gundy-Davis' inequality and Chevalier's inequality. Moreover,
we investigate some other equivalent relations between variable exponent
martingale Hardy spaces.
Archive classification: math.FA
Submitted from: pdliu at whu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.8146
or
http://arXiv.org/abs/1412.8146
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando, Andreas Defant, and Pablo
Sevilla-Peris
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 30 Dec 2014 17:33:37 -0600
To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>
This is an announcement for the paper "Almost sure-sign convergence
of Hardy-type Dirichlet series" by Daniel Carando, Andreas Defant,
and Pablo Sevilla-Peris.
Abstract:
Hartman proved in 1939 that the width of the largest possible strip
in the complex plane, on which a Dirichlet series $\sum_n a_n n^{-s}$ is
uniformly a.s.-sign convergent (i.e., $\sum_n \varepsilon_n a_n n^{-s}$
converges uniformly for almost all sequences of signs $\varepsilon_n
=\pm 1$) but does not convergent absolutely, equals $1/2$. We study this
result from a more modern point of view within the framework of so called
Hardy-type Dirichlet series with values in a Banach space.
Archive classification: math.FA
Mathematics Subject Classification: 30B50, 30H10, 46G20
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/1412.5030
or
http://arXiv.org/abs/1412.5030
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Liran Rotem
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 30 Dec 2014 17:35:04 -0600
To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>
This is an announcement for the paper "A letter: The log-Brunn-Minkowski
inequality for complex bodies" by Liran Rotem.
Abstract:
In this short note we explain why the log-Brunn-Minkowski conjecture is
correct for complex convex bodies. We do this by relating the conjecture
to the notion of complex interpolation, and appealing to a general
theorem by Cordero-Erausquin.
Archive classification: math.MG math.FA
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/1412.5321
or
http://arXiv.org/abs/1412.5321
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Karl-Mikael Perfekt
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 30 Dec 2014 17:36:06 -0600
To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>
This is an announcement for the paper "On M-ideals and o-O type spaces"
by Karl-Mikael Perfekt.
Abstract:
We consider pairs of Banach spaces (M_0, M) such that M_0 is defined
in terms of a little-o condition, and M is defined by the corresponding
big-O condition. The construction is general and pairs include function
spaces of vanishing and bounded mean oscillation, vanishing weighted and
weighted spaces of functions or their derivatives, M\"obius invariant
spaces of analytic functions, Lipschitz-H\"older spaces, etc. It has
previously been shown that the bidual M_0** of M_0 is isometrically
isomorphic with M. The main result of this paper is that M_0 is an
M-ideal in M. This has several useful consequences: M_0 has Pelczynskis
properties (u) and (V), M_0 is proximinal in M, and M_0* is a strongly
unique predual of M, while M_0 itself never is a strongly unique predual.
Archive classification: math.FA
Remarks: 9 pages
Submitted from: karlmikp at math.ntnu.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.5486
or
http://arXiv.org/abs/1412.5486
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ersin Kizgut, Elif Uyanik, and Murat Yurdakul
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 30 Dec 2014 17:37:14 -0600
To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>
This is an announcement for the paper "On operator relations between
locally convex spaces" by Ersin Kizgut, Elif Uyanik, and Murat Yurdakul.
Abstract:
A linear operator $T:X \to Y$ between vector spaces is called strictly
singular if for any infinite dimensional closed vector subspace $M$ of
$X$, the restriction of $T$ on $M$ is not a topological isomorphism. In
this note we introduced some sufficient conditions on domain and range
spaces such that any bounded linear operator in between is strictly
singular, and give some examples of spaces satisfying these conditions.
Archive classification: math.FA
Remarks: 15 pages, presented in the context of 8th Australian and New
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.5761
or
http://arXiv.org/abs/1412.5761
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii and Beata
Randrianantoanina
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 30 Dec 2014 17:38:37 -0600
To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>
This is an announcement for the paper "Metric spaces admitting
low-distortion embeddings into all $n$-dimensional Banach spaces" by
Mikhail I. Ostrovskii and Beata Randrianantoanina.
Abstract:
For a fixed $K\gg 1$ and $n\in\mathbb{N}$, $n\gg 1$, we study metric
spaces which admit embeddings with distortion $\le K$ into each
$n$-dimensional Banach space. Classical examples include spaces embeddable
into $\log n$-dimensional Euclidean spaces, and equilateral spaces.
We prove that good embeddability properties are preserved under
the operation of metric composition of metric spaces. In particular,
we prove that any $n$-point ultrametric can be embedded with uniformly
bounded distortion into any Banach space of dimension $\log n$.
The main result of the paper is a new example of a family of finite
metric spaces which are not metric compositions of classical examples and
which do embed with uniformly bounded distortion into any Banach space
of dimension $n$. This partially answers a question of G.~Schechtman.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12,
30L05, 46B15, 52A21
Remarks: 35 pages, 4 figures
Submitted from: randrib at miamioh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.7670
or
http://arXiv.org/abs/1412.7670
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Brendan Pass and Susanna Spektor
From: Dale Alspach <alspach at math.okstate.edu>
Date: Tue, 30 Dec 2014 17:39:38 -0600
To: <alspach at math.okstate.edu>, <banach at mathdept.okstate.edu>
This is an announcement for the paper "On Khinchine type inequalities
for pairwise independent Rademacher random variables" by Brendan Pass
and Susanna Spektor.
Abstract:
We consider Khintchine type inequalities on the $p$-th moments of
vectors of $N$ pairwise independent Rademacher random variables. We
establish that an analogue of Khintchine's inequality cannot hold in this
setting with a constant that is independent of $N$; in fact, we prove that
the best constant one can hope for is at least $N^{1/2-1/p}$. Furthermore,
we show that this estimate is sharp for exchangeable vectors when $p =
4$. As a fortunate consequence of our work, we obtain similar results
for $3$-wise independent vectors.
Archive classification: math.FA math.PR
Submitted from: sanaspek at yandex.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.7859
or
http://arXiv.org/abs/1412.7859
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