Messages from 2011
These are the messages distributed to the Banach list during 2011.
Return-path: <alspach at math.okstate.edu>
From: Bill Johnson <johnson at math.tamu.edu>
Subject: [Banach] 2011 Workshop at A&M
Date: Fri, 28 Jan 2011 05:46:15 -0600 (CST)
To: banach at math.okstate.edu
Workshop in Analysis and Probability
Department of Mathematics
Texas A&M University
Summer 2011
The Summer 2011 Workshop in Analysis and Probability at Texas A&M
University will be in session from July 5 until August 5. For information
about the Workshop, consult the Workshop Home Page, whose URL is
http://www.math.tamu.edu/conferences/linanalysis/
The Informal Regional Functional Analysis Seminar (SUMIRFAS) will be held
July 29 - 31.
Steve Dilworth, Daniel Freeman, Denka Kuzarova, Edward Odell (co-chair),
and Thomas Schlumprecht (co-chair) are organizing a Concentration Week on
"Greedy Algorithms in Banach spaces and Compressed Sensing" for the week
of July 18-22. When encoding or reconstructing a vector using an iterative
algorithm, a natural
approach is to take the best or biggest approximation at each iteration.
Such techniques are referred to as greedy algorithms. The theory of
compressed sensing is concerned with encoding and reconstructing vectors
which are sparsely represented with respect to a given basis. Kevin Ford
will present a series of talks on deterministic construction of matrices
with the restrictive isometry property. There will be a second series of
talks devoted to greedy algorithms and bases. The home page for this
Concentration Week is at
http://www.math.utexas.edu/users/freeman/greedy11/index.html
Florent Baudier (chair), Bill Johnson, Piotr Nowak, and Bunyamin Sari are
organizing a Concentration Week on "Non-Linear Geometry of Banach Spaces,
Geometric Group Theory, and Differentiability" for the week of August 1-5.
The program will include an introductory course by Mark Sapir on coarse
embeddings and their applications to geometric group theory, and a series
of lectures by Gilles Godefroy on the recent work of the late Nigel Kalton
on the coarse classification of Banach spaces. The home page for this
Concentration Week is at
http://www.math.tamu.edu/~pnowak/index/cw.html
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
Larson <larson at math.tamu.edu>, Gilles Pisier <pisier at math.tamu.edu>, or
Joel Zinn <jzinn at math.tamu.edu>.
For information about the Concentration Week "Greedy Algorithms in Banach
spaces and Compressed Sensing", contact Thomas Schlumprecht
<schlump at math.tamu.edu> or Ted Odell <odell at mail.ma.utexas.edu>.
For information about the Concentration Week "Non-Linear Geometry of
Banach Spaces, Geometric Group Theory, and Differentiability", contact
Florent Baudier <florent at math.tamu.edu>.
_______________________________________________
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From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Marek Cuth
Date: Fri, 28 Jan 2011 17:15:39 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Separable reduction theorems by
the method of elementary submodels" by Marek Cuth.
Abstract: We introduce an interesting method of proving separable
reduction theorems - the method of elementary submodels. We are studying
whether it is true that a set (function) has given property if and only
if it has this property with respect to a special separable subspace,
dependent only on the given set (function). We are interested in
properties of sets ``to be dense, nowhere dense, meager, residual or
porous'' and in properties of functions ``to be continuous, semicontinuous
or Fr\'echet differentiable''. Our method of creating separable subspaces
enables us to combine our results, so we easily get separable reductions
of function properties such as ``be continuous on a dense subset'',
``be Fr\'echet differentiable on a residual subset'', etc. Finally,
we show some applications of presented separable reduction theorems and
demonstrate that some results of Zajicek, Lindenstrauss and Preiss hold
in nonseparable setting as well.
Archive classification: math.FA
Mathematics Subject Classification: 46B26, 03C30
Remarks: 27 pages
Submitted from: cuthm5am at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.1627
or
http://arXiv.org/abs/1101.1627
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Adriano Thiago L. Bernardino and Daniel
Pellegrino
Date: Fri, 28 Jan 2011 17:18:07 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some remarks on absolutely
summing multilinear operators" by Adriano Thiago L. Bernardino and
Daniel Pellegrino.
Abstract: This short note has a twofold purpose: (i) to answer a
question from a recent paper of D. Popa on multilinear variants of
Pietsch's composition theorem for absolutely summing operators. More
precisely, we show that there is a natural (and very simple) perfect
extension of Pietsch's composition theorem to the multilinear setting;
(ii) to investigate extensions of some results of the aforementioned
paper for particular situations, by exploring cotype properties of the
spaces involved.
Archive classification: math.FA
Remarks: 7 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.2119
or
http://arXiv.org/abs/1101.2119
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Daniel Pellegrino and Joilson Ribeiro
Date: Fri, 28 Jan 2011 17:19:31 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On multi-ideals and polynomial
ideals of Banach spaces" by Daniel Pellegrino and Joilson Ribeiro.
Abstract: The notion of coherent sequences of polynomial ideals and
the notion of compatibility of a polynomial ideal with a given operator
ideal were recently introduced by D. Carando, V. Dimant and S. Muro. These
concepts play an important role in the theory of polynomial ideals, since
they offer some properties that polynomial ideals must satisfy in order
to keep the spirit of a given operator ideal and also maintain some
coherence between the different levels of $n$-homogeneity. However,
it seems to exist no reason to omit the multi-ideals from these
cycle of ideas. In the present paper we revisit these notions; more
precisely, we propose that these concepts are considered for a pair
$(\mathcal{P}_{k},\mathcal{M}_{k})_{k=1}^{\infty}$, where $(\mathcal{P}%
_{k})_{k=1}^{\infty}$ is a polynomial ideal and $(\mathcal{M}_{k}%
)_{k=1}^{\infty}$ is a multi-ideal. The construction of our approach is
inspired by the important special case of absolutely summing operators.
Archive classification: math.FA
Remarks: 16 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.1992
or
http://arXiv.org/abs/1101.1992
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Ngai-Ching Wong
Date: Fri, 28 Jan 2011 17:21:46 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Operator ideals arising from
generating sequences" by Ngai-Ching Wong.
Abstract: In this note, we will discuss how to relate an operator ideal
on Banach spaces to the sequential structures it defines. Concrete
examples of ideals of compact, weakly compact, completely continuous,
Banach-Saks and weakly Banach-Saks operators will be demonstrated.
Archive classification: math.FA
Mathematics Subject Classification: 47L20, 47B10 46A11, 46A17
Remarks: 17 pages, for the Proceedings of International Conference on
Algebra 2010, World Scientific. (The International Conference on Algebra
in honor of the 70th birthday of Professor Shum Kar Ping was held by
Universitas Gadjah Mada (UGM)in Yogyakarta, Indonesia on October 7-10,
2010.)
Submitted from: wong at math.nsysu.edu.tw
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.2085
or
http://arXiv.org/abs/1101.2085
Return-path: <alspach at math.okstate.edu>
From: alspach at math.okstate.edu (Dale Alspach)
Subject: Abstract of a paper by Daniel Carando, Silvia Lassalle, and Pablo
Schmidberg
Date: Fri, 28 Jan 2011 17:23:40 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The reconstruction formula for
Banach frames and duality" by Daniel Carando, Silvia Lassalle, and
Pablo Schmidberg.
Abstract: We study conditions on a Banach frame that ensures the validity
of a reconstruction formula. In particular, we show that any Banach frames
for (a subspace of) $L_p$ or $L_{p,q}$ ($1\le p < \infty$) with respect
to a solid sequence space always satisfies an unconditional reconstruction
formula. The existence of reconstruction formulae allows us to prove some
James-type results for atomic decompositions: an unconditional atomic
decomposition (or unconditional Schauder frame) for $X$ is shrinking
(respectively, boundedly complete) if and only if $X$ does not contain
an isomorphic copy of $\ell_1$ (respectively, $c_0$).
Archive classification: math.FA math.CA
Mathematics Subject Classification: 41A65, 42C15, 46B10, 46B15
Remarks: 16 pages
Submitted from: slassall at dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.2430
or
http://arXiv.org/abs/1101.2430
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:12:07 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Grothendieck's Theorem, past and
present" by Gilles Pisier.
Abstract: Probably the most famous of Grothendieck's contributions to
Banach space theory is the result that he himself described as ``the
fundamental theorem in the metric theory of tensor products''. That is
now commonly referred to as ``Grothendieck's theorem'' (GT in short),
or sometimes as ``Grothendieck's inequality''. This had a major impact
first in Banach space theory (roughly after 1968), then, later on,
in $C^*$-algebra theory, (roughly after 1978). More recently, in this
millennium, a new version of GT has been successfully developed in the
framework of ``operator spaces'' or non-commutative Banach spaces. In
addition, GT independently surfaced in several quite unrelated fields:\
in connection with Bell's inequality in quantum mechanics, in graph
theory where the Grothendieck constant of a graph has been introduced
and in computer science where the Grothendieck inequality is invoked
to replace certain NP hard problems by others that can be treated by
``semidefinite programming' and hence solved in polynomial time. In this
expository paper, we present a review of all these topics, starting from
the original GT. We concentrate on the more recent developments and merely
outline those of the first Banach space period since detailed accounts
of that are already available, for instance the author's 1986 CBMS notes.
Archive classification: math.FA math-ph math.MP math.OA
Mathematics Subject Classification: 46B28, 46B07
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.4195
or
http://arXiv.org/abs/1101.4195
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by H. Garth Dales, Matthew Daws, Hung Le Pham,
Paul Ramsden
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:13:33 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Multi-norms and the injectivity
of $L^p(G)$" by H. Garth Dales, Matthew Daws, Hung Le Pham, Paul Ramsden.
Abstract: Let $G$ be a locally compact group, and take
$p\in(1,\infty)$. We prove that the Banach left $L^1(G)$-module $L^p(G)$
is injective (if and) only if the group $G$ is amenable. Our proof uses
the notion of multi-norms. We also develop the theory of multi-normed
spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46H25, 43A20
Remarks: 27 pages
Submitted from: matt.daws at cantab.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.4320
or
http://arXiv.org/abs/1101.4320
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:14:57 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sparse quadratic forms and
their geometric applications (after Batson, Spielman and Srivastava)"
by Assaf Naor.
Abstract: We survey the work of Batson, Spielman and Srivastava on
graph sparsification, and we describe some of its recently discovered
geometric applications.
Archive classification: math.FA
Remarks: appeared as s\'eminaire Bourbaki expos\'e no. 1033, 2011
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/1101.4324
or
http://arXiv.org/abs/1101.4324
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Guohui Song, Haizhang Zhang, Fred J.
Hickernell
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:16:32 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Reproducing kernel Banach spaces
with the l1 norm" by Guohui Song, Haizhang Zhang, Fred J. Hickernell.
Abstract: Targeting at sparse learning, we construct Banach spaces B of
functions on an input space X with the properties that (1) B possesses
an l1 norm in the sense that it is isometrically isomorphic to the
Banach space of integrable functions on X with respect to the counting
measure; (2) point evaluations are continuous linear functionals on B
and are representable through a bilinear form with a kernel function;
(3) regularized learning schemes on B satisfy the linear representer
theorem. Examples of kernel functions admissible for the construction
of such spaces are given.
Archive classification: stat.ML cs.LG math.FA
Submitted from: zhhaizh2 at sysu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.4388
or
http://arXiv.org/abs/1101.4388
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Guohui Song, Haizhang Zhang
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:18:43 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Reproducing kernel Banach
spaces with the l1 norm II: Error analysis for regularized least square
regression" by Guohui Song, Haizhang Zhang.
Abstract: A typical approach in estimating the learning rate of a
regularized learning scheme is to bound the approximation error by the
sum of the sampling error, the hypothesis error and the regularization
error. Using a reproducing kernel space that satisfies the linear
representer theorem brings the advantage of discarding the hypothesis
error from the sum automatically. Following this direction, we illustrate
how reproducing kernel Banach spaces with the l1 norm can be applied
to improve the learning rate estimate of l1-regularization in machine
learning.
Archive classification: stat.ML cs.LG math.FA
Submitted from: zhhaizh2 at sysu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.4439
or
http://arXiv.org/abs/1101.4439
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Fresen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:29:25 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A multivariate Gnedenko law of
large numbers" by Daniel Fresen.
Abstract: We show that the convex hull of a large i.i.d. sample from a
non-vanishing log-concave distribution approximates a pre-determined
body in the logarithmic Hausdorff distance and in the Banach-Mazur
distance. For p-log-concave distributions with p>1 (such as the normal
distribution where p=2) we also have approximation in the Hausdorff
distance. These are multivariate versions of the Gnedenko law of large
numbers which gaurantees concentration of the maximum and minimum in the
one dimensional case. We give three different deterministic bodies that
serve as approximants to the random body. The first is the floating body
that serves as a multivariate quantile, the second body is given as a
contour of the density function, and the third body is given in terms
of the Radon transform. We end the paper by constructing a probability
measure with an interesting universality property.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60D05, 60F99, 52A20, 52A22, 52B11
Remarks: 18 pages
Submitted from: djfb6b at mail.missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.4887
or
http://arXiv.org/abs/1101.4887
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boris Rubin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:30:50 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Elementary inversion of Riesz
potentials and Radon-John transforms" by Boris Rubin.
Abstract: New simple proofs are given to some elementary approximate
and explicit inversion formulas for Riesz potentials. The results are
applied to reconstruction of functions from their integrals over
Euclidean planes in integral geometry.
Archive classification: math.FA
Remarks: 9 pages
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.5105
or
http://arXiv.org/abs/1101.5105
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Thiago L. Bernardino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:31:57 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Remarks on cotype absolutely
summing multilinear operators" by A. Thiago L. Bernardino.
Abstract: In this short note we present some new results concerning
cotype and absolutely summing multilinear operators.
Archive classification: math.FA
Remarks: 5 pages
Submitted from: thiagodcea at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.5119
or
http://arXiv.org/abs/1101.5119
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cleon S. Barroso, Ondrej F.K. Kalenda and
Pei-Kee Lin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:33:26 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the approximate fixed point
property in abstract spaces" by Cleon S. Barroso, Ondrej F.K. Kalenda
and Pei-Kee Lin.
Abstract: Let $X$ be a Hausdorff topological vector space, $X^*$
its topological dual and $Z$ a subset of $X^*$. In this paper, we
establish some results concerning the $\sigma(X,Z)$-approximate fixed
point property for bounded, closed convex subsets $C$ of $X$. Three
major situations are studied. First when $Z$ is separable in the strong
topology. Second when $X$ is a metrizable locally convex space and
$Z=X^*$, and third when $X$ is not necessarily metrizable but admits
a metrizable locally convex topology compatible with the duality. Our
approach focuses on establishing the Fr\'echet-Urysohn property for
certain sets with regarding the $\sigma(X,Z)$-topology. The support tools
include the Brouwer's fixed point theorem and an analogous version of
the classical Rosenthal's $\ell_1$-theorem for $\ell_1$-sequences in
metrizable case. The results are novel and generalize previous work
obtained by the authors in Banach spaces.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 47H10, 46A03
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/1101.5274
or
http://arXiv.org/abs/1101.5274
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Maxim V. Balashov and Dusan Repovs
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:35:01 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Uniformly convex subsets of the
Hilbert space with modulus of convexity of the second order" by Maxim
V. Balashov and Dusan Repovs.
Abstract: We prove that in the Hilbert space every uniformly convex set
with modulus of convexity of the second order at zero is an intersection
of closed balls of fixed radius. We also obtain an estimate of this
radius.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46C05, 54C60, 46N10, 32F17
Citation: J. Math. Anal. Appl. 377:2 (2011), 754-761
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Matthew Daws, Richard Haydon, Thomas
Schlumprecht, and Stuart White
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:36:39 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Shift invariant preduals of
$\ell_1(\Z)$" by Matthew Daws, Richard Haydon, Thomas Schlumprecht,
and Stuart White.
Abstract: The Banach space $\ell_1(\Z)$ admits many non-isomorphic
preduals, for example, $C(K)$ for any compact countable space $K$, along
with many more exotic Banach spaces. In this paper, we impose an extra
condition: the predual must make the bilateral shift on $\ell_1(\Z)$
weak$^*$-continuous. This is equivalent to making the natural convolution
multiplication on $\ell_1(\Z)$ separately weak$*$-continuous and so
turning $\ell_1(\Z)$ into a dual Banach algebra. We call such preduals
\emph{shift-invariant}. It is known that the only shift-invariant predual
arising from the standard duality between $C_0(K)$ (for countable locally
compact $K$) and $\ell_1(\Z)$ is $c_0(\Z)$. We provide an explicit
construction of an uncountable family of distinct preduals which do make
the bilateral shift weak$^*$-continuous. Using Szlenk index arguments,
we show that merely as Banach spaces, these are all isomorphic to
$c_0$. We then build some theory to study such preduals, showing that
they arise from certain semigroup compactifications of $\Z$. This allows
us to produce a large number of other examples, including non-isometric
preduals, and preduals which are not Banach space isomorphic to $c_0$.
Archive classification: math.FA
Remarks: 31 pages
Submitted from: matt.daws at cantab.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1101.5696
or
http://arXiv.org/abs/1101.5696
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Detelin Dosev, William B. Johnson, and
Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:38:37 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Commutators on $L_p$, $1\le
p<\infty$" by Detelin Dosev, William B. Johnson, and Gideon Schechtman.
Abstract: The operators on $\LP=L_p[0,1]$, $1\leq p<\infty$, which are
not commutators are those of the form $\lambda I + S$ where
$\lambda\neq 0$ and $S$ belongs to the largest ideal in $\opLP$. The
proof involves new structural results for operators on $\LP$ which are of
independent interest.
Archive classification: math.FA
Mathematics Subject Classification: 47B47, 46E30
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/1102.0137
or
http://arXiv.org/abs/1102.0137
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Roman Vershynin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 4 Feb 2011 10:39:56 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Invertibility of symmetric random
matrices" by Roman Vershynin.
Abstract: Let H be an n by n symmetric random matrix whose above-diagonal
entries are general iid random variables (possibly discrete) with zero
mean, unit variance, and subgaussian tail decay. We prove that H is
singular with probability at most exp(n^{-c}) for some constant c>0,
and that the spectral norm of the inverse of H is O(\sqrt{n}) with high
probability. More generally, the spectrum of H is delocalized -- with
high probability, there are no eigenvalues in an arbitrary fixed interval
of the optimal length o(n^{-1/2}). The delocalization result also holds
under the fourth moment assumption on the entries of H. These results
improve upon the polynomial singularity bound O(n^{-1/8+epsilon}) due
to Costello, Tao and Vu, and they generalize, up to constant factors,
previous results for distributions whose first few moments match the
moments of the normal distribution (due to the universality results of
Tao and Vu) and for continuous distributions in the bulk of the spectrum
(due to Erd\"os, Schlein and Yau).
Archive classification: math.PR math.FA
Mathematics Subject Classification: 15B52
Remarks: 52 pages
Submitted from: romanv at umich.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.0300
or
http://arXiv.org/abs/1102.0300
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Richard J. Smith
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:26:34 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Tree duplicates,
$G_\delta$-diagonals and Gruenhage spaces" by Richard J. Smith.
Abstract: We present an example in ZFC of a locally compact, scattered
Hausdorff non-Gruenhage space $D$ having a $\G_delta$-diagonal. This
answers a question posed by Orihuela, Troyanski and the author in a study
of strictly convex norms on Banach spaces. In addition, we show that the
Banach space of continuous functions $C_0(D)$ admits a $C^\infty$-smooth
bump function.
Archive classification: math.FA math.GN
Submitted from: richard.smith at ucd.ie
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.0982
or
http://arXiv.org/abs/1102.0982
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ralf Beckmann and Anton Deitmar
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:28:00 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strong vector valued integrals"
by Ralf Beckmann and Anton Deitmar.
Abstract: Strong Bochner type integrals with values in locally convex
spaces are introduced. It is shown that the strong integral exists in the
same cases as the weak (Gelfand-Pettis) integral is known to exist. The
strong integral has better continuity properties that the weak integral.
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/1102.1246
or
http://arXiv.org/abs/1102.1246
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Pellegrino and Joilson Ribeiro
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:29:58 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On everywhere almost summing
multilinear operators" by Daniel Pellegrino and Joilson Ribeiro.
Abstract: In this paper we obtain new results and characterizations for
the classes (ideals) of everywhere almost summing multilinear operators
and everywhere almost summing $n$-homogeneous polynomials. Among other
results we prove that the ideal of everywhere almost summing polynomials
is a global holomorphy type (this is not true for the original concept
of almost summing polynomials).
Archive classification: math.FA
Remarks: 10 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.1460
or
http://arXiv.org/abs/1102.1460
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Fresen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:31:03 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Comments on the floating body
and the hyperplane conjecture" by Daniel Fresen.
Abstract: We provide upper and lower bounds on the logarithmic Hausdorff
distance between an arbitrary convex body $K\subset \mathbb{R}^{d}$\ and
the convex floating body $K_{\delta }$ inside $K$. We also discuss the
hyperplane conjecture (the slicing problem) and provide a reformulation
of this famous unsolved mystery in terms of the floating body.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 52A23, 52A20, 52A21, 52A38
Remarks: 8 pages
Submitted from: djfb6b at mail.missouri.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.2570
or
http://arXiv.org/abs/1102.2570
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Guillaume Aubrun and Ion Nechita
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:32:16 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The multiplicative property
characterizes $\ell_p$ and $L_p$ norms" by Guillaume Aubrun and Ion
Nechita.
Abstract: We show that $\ell_p$ norms are characterized as the unique
norms which are both invariant under coordinate permutation and
multiplicative with respect to tensor products. Similarly, the $L_p$
norms are the unique rearrangement-invariant norms on a probability space
such that $\|X Y\|=\|X\|\cdot\|Y\|$ for every pair $X,Y$ of independent
random variables. Our proof relies on Cram\'er's large deviation theorem.
Archive classification: math.FA
Remarks: 8 pages, 1 figure
Submitted from: inechita at uottawa.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.2618
or
http://arXiv.org/abs/1102.2618
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Franck Barthe, Chiara Bianchini, and Andrea
Colesanti
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:38:42 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isoperimetry and stability of
hyperplanes for product probability measures" by Franck Barthe, Chiara
Bianchini, and Andrea Colesanti.
Abstract: We investigate stationarity and stability of half-spaces as
isoperimetric sets for product probability measures, considering the
cases of coordinate and non-coordinate half-spaces. Moreover, we present
several examples to which our results can be applied, with a particular
emphasis on the logistic measure.
Archive classification: math.FA math.PR
Submitted from: chiara.bianchini at iecn.u-nancy.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.3621
or
http://arXiv.org/abs/1102.3621
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Veronica Dimant and Silvia Lassalle
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:40:07 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$M$-structures in vector-valued
polynomial spaces" by Veronica Dimant and Silvia Lassalle.
Abstract: This paper is concerned with the study of $M$-structures
in spaces of polynomials. More precisely, we discuss for $E$ and $F$
Banach spaces, whether the class of weakly continuous on bounded sets
$n$-homogeneous polynomials, $\mathcal P_w(^n E, F)$, is an $M$-ideal
in the space of continuous $n$-homogeneous polynomials $\mathcal P(^n
E, F)$. We show that there is some hope for this to happen only for a
finite range of values of $n$. We establish sufficient conditions under
which the problem has positive and negative answers and use the obtained
results to study the particular cases when $E=\ell_p$ and $F=\ell_q$ or
$F$ is a Lorentz sequence space $d(w,q)$. We extend to our setting the
notion of property $(M)$ introduced by Kalton which allows us to lift
$M$-structures from the linear to the vector-valued polynomial context.
Also, when $\mathcal P_w(^n E, F)$ is an $M$-ideal in $\mathcal P(^n E,
F)$ we prove a Bishop-Phelps type result for vector-valued polynomials and
relate norm-attaining polynomials with farthest points and remotal sets.
Archive classification: math.FA
Mathematics Subject Classification: 47H60, 46B04, 47L22, 46B20
Submitted from: vero at udesa.edu.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.3850
or
http://arXiv.org/abs/1102.3850
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stefano Rossi
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:41:21 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On a class of $C^*$ preduals of
$l_1$" by Stefano Rossi.
Abstract: Some nice preduals of $l_1$ are presented
Archive classification: math.FA
Remarks: 5 pages
Submitted from: s-rossi at mat.uniroma1.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.4325
or
http://arXiv.org/abs/1102.4325
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Thiago Lopes Bernardino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:42:43 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On cotype and inclusions for
absolutely summing multilinear operators" by A. Thiago Lopes Bernardino.
Abstract: In this note we improve previous results on inclusion theorems
for absolutely summing multilinear operators.
Archive classification: math.FA
Remarks: 3 pages
Submitted from: thiagodcea at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.4542
or
http://arXiv.org/abs/1102.4542
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jin Xi Chen, Zi Li Chen and Guo Xing Ji
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:44:11 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Order continuous extensions of
positive compact operators on Banach lattices" by Jin Xi Chen, Zi Li
Chen and Guo Xing Ji.
Abstract: Let $E$ and $F$ be Banach lattices. Let $G$ be a vector
sublattice of $E$ and $T: G\rightarrow F$ be an order continuous
positive compact (resp. weakly compact) operators. We show that if $G$
is an ideal or an order dense sublattice of $E$, then $T$ has a norm
preserving compact (resp. weakly compact) positive extension to $E$
which is likewise order continuous on $E$. In particular, we prove that
every compact positive orthomorphism on an order dense sublattice of $E$
extends uniquely to a compact positive orthomorphism on $E$.
Archive classification: math.FA
Remarks: 7 pages
Submitted from: jinxichen at home.swjtu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.4912
or
http://arXiv.org/abs/1102.4912
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:45:38 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On metric characterizations of
some classes of Banach spaces" by Mikhail Ostrovskii.
Abstract: The paper contains the following results and observations:
(1) There exists a sequence of unweighted graphs $\{G_n\}_n$ with
maximum degree $3$ such that a Banach space $X$ has no nontrivial
cotype iff $\{G_n\}_n$ admit uniformly bilipschitz embeddings into $X$;
(2) The same for Banach spaces with no nontrivial type; (3) A sequence
$\{G_n\}$ characterizing Banach spaces with no nontrivial cotype in
the sense described above can be chosen to be a sequence of bounded
degree expanders; (4) The infinite diamond does not admit a bilipschitz
embedding into Banach spaces with the Radon-Nikod\'{y}m property; (5) A
new proof of the Cheeger-Kleiner result: The Laakso space does not admit
a bilipschitz embedding into Banach spaces with the Radon-Nikod\'{y}m
property; (6) A new proof of the Johnson-Schechtman result: uniform
bilipschitz embeddability of finite diamonds into a Banach space implies
its nonsuperreflexivity.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 46B85, Secondary: 05C12, 46B07,
46B22, 54E35
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.5082
or
http://arXiv.org/abs/1102.5082
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Greg Kuperberg
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:47:48 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Norms as a function of p are
linearly independent in finite dimensions" by Greg Kuperberg.
Abstract: We show that there are no non-trivial linear dependencies
among p-norms of vectors in finite dimensions that hold for all p. The
proof is by analytic continuation and a theorem of Ritt.
Archive classification: math.FA
Remarks: 1 page, 1 figure
Submitted from: greg at math.ucdavis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.5026
or
http://arXiv.org/abs/1102.5026
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Remi Gribonval and Morten Nielsen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Feb 2011 16:52:43 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The restricted isometry property
meets nonlinear approximation with redundant frames" by Remi Gribonval
and Morten Nielsen.
Abstract: It is now well known that sparse or compressible vectors can
be stably recovered from their low-dimensional projection, provided the
projection matrix satisfies a Restricted Isometry Property (RIP). We
establish new implications of the RIP with respect to nonlinear
approximation in a Hilbert space with a redundant frame. The main
ingredients of our approach are: a) Jackson and Bernstein inequalities,
associated to the characterization of certain approximation spaces
with interpolation spaces; b) a new proof that for overcomplete frames
which satisfy a Bernstein inequality, these interpolation spaces are
nothing but the collection of vectors admitting a representation in
the dictionary with compressible coefficients; c) the proof that the
RIP implies Bernstein inequalities. As a result, we obtain that in most
overcomplete random Gaussian dictionaries with fixed aspect ratio, just
as in any orthonormal basis, the error of best $m$-term approximation of
a vector decays at a certain rate if, and only if, the vector admits a
compressible expansion in the dictionary. Yet, for mildly overcomplete
dictionaries with a one-dimensional kernel, we give examples where the
Bernstein inequality holds, but the same inequality fails for even the
smallest perturbation of the dictionary.
Archive classification: math.FA
Report Number: RR-7548
Remarks: This work has been submitted for possible publication. Copyright
be transferred without notice, after which this version may no longer
be accessible.
Submitted from: remi.gribonval at inria.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1102.5324
or
http://arXiv.org/abs/1102.5324
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Frank Bonsall
From: Jonathan Partington <J.R.Partington at leeds.ac.uk>
Date: Mon, 28 Feb 2011 22:45:24 +0000
To: "banach at cauchy.math.okstate.edu" <banach at math.okstate.edu>
We regret to say that Professor Frank Bonsall FRS, well known for his
work in functional analysis, in particular, Banach algebras, numerical
ranges and operator theory, died in Harrogate, Yorkshire on Tuesday
February 22nd. He was 90 years old.
Jonathan Partington, University of Leeds, UK
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] M. Kadec
From: Vladimir Kadets <vova1kadets at yahoo.com>
Date: Mon, 7 Mar 2011 02:28:14 -0800 (PST) (04:28 CST)
To: Banach at math.okstate.edu
I regret to inform that my father
Professor Mikhail Kadets (M. Kadec)
died on Monday, March 7.
He was 87 years old.
Vladimir Kadets.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ran Levy and Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:18:21 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stabilizing isomorphisms from
$\ell_p(\ell_2)$ into $L_p[0,1]$" by Ran Levy and Gideon Schechtman.
Abstract: Let $1<p\not=2<\infty$, $\epsilon>0$ and let
$T:\ell_p(\ell_2)\overset{into}{\rightarrow}L_p[0,1]$ be an
isomorphism. Then there is a subspace $Y\subset \ell_p(\ell_2)$
$(1+\epsilon)$-isomorphic to $\ell_p(\ell_2)$ such that: $T_{|Y}$ is an
$(1+\epsilon)$-isomorphism and $T\left(Y\right)$ is $K_p$-complemented
in $L_p[0,1]$, with $K_p$ depending only on $p$. Moreover, $K_p\le
(1+\epsilon)\gamma_p$ if $p>2$ and $K_p\le (1+\epsilon)\gamma_{p/(p-1)}$
if $1<p<2$, where $\gamma_r$ is the $L_r$ norm of a standard Gaussian
variable.
Archive classification: math.FA
Mathematics Subject Classification: 46E30
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/1103.0047
or
http://arXiv.org/abs/1103.0047
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:19:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximate Gaussian isoperimetry
for k sets" by Gideon Schechtman.
Abstract: Given $2\le k\le n$, the minimal $(n-1)$-dimensional Gaussian
measure of the union of the boundaries of $k$ disjoint sets of equal
Gaussian measure in $\R^n$ whose union is $\R^n$ is of order $\sqrt{\log
k}$. A similar results holds also for partitions of the sphere $S^{n-1}$
into $k$ sets of equal Haar measure.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60E15, 52A40
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/1102.4102
or
http://arXiv.org/abs/1102.4102
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, 21 Mar 2011 11:21:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Measurability in C(2^k) and Kunen
cardinals" by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez.
Abstract: A cardinal k is called a Kunen cardinal if the sigma-algebra
on k x k generated by all products AxB, coincides with the power set
of k x k. For any cardinal k, let C(2^k) be the Banach space of all
continuous real-valued functions on the Cantor cube 2^k. We prove that k
is a Kunen cardinal if and only if the Baire sigma-algebra on C(2^k) for
the pointwise convergence topology coincides with the Borel sigma-algebra
on C(2^k) for the norm topology. Some other links between Kunen cardinals
and measurability in Banach spaces are also given.
Archive classification: math.FA
Mathematics Subject Classification: 28A05, 28B05
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.0247
or
http://arXiv.org/abs/1103.0247
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marek Kosiek and Krzysztof Rudol
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:23:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A disintegration theorem" by
Marek Kosiek and Krzysztof Rudol.
Abstract: A new approach to disintegration of measures is presented,
allowing one to drop the usually taken separability assumption. The main
tool is a result on fibers in the spectrum of algebra of essentially
bounded functions established recently by the first-named author.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 28A50, Secondary: 46J10
Remarks: 3 pages
Submitted from: Marek.Kosiek at im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.0255
or
http://arXiv.org/abs/1103.0255
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pericles D Pavlakos and Minos Petrakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:24:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the structure of non dentable
subsets of C({\omega}^{\omega}^k)" by Pericles D Pavlakos and Minos
Petrakis.
Abstract: It is shown that there is no K closed convex bounded
non-dentable subset of C({\omega}^{\omega} ^k) such that on the subsets
of K the PCP and the RNP are equivalent properties. Then applying
Schachermayer-Rosenthal theorem, we conclude that every non-dentable K
contains non-dentable subset L so that on L the weak topology coincides
with the norm one. It follows from known results that the RNP and the
KMP are equivalent properties on the subsets of C({\omega}^{\omega} ^k).
Archive classification: math.FA
Remarks: 18 pages,accepted in Studia Mathematica
Submitted from: minos at science.tuc.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.0366
or
http://arXiv.org/abs/1103.0366
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Radoslaw Adamczak, Rafal Latala, Alexander
E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:27:05 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometry of log-concave
ensembles of random matrices and approximate reconstruction" by
Radoslaw Adamczak, Rafal Latala, Alexander E. Litvak, Alain Pajor,
and Nicole Tomczak-Jaegermann.
Abstract: We study the Restricted Isometry Property of a random matrix
$\Gamma$ with independent isotropic log-concave rows. To this end, we
introduce a parameter $\Gamma_{k,m}$ that controls uniformly the operator
norm of sub-matrices with $k$ rows and $m$ columns. This parameter is
estimated by means of new tail estimates of order statistics and deviation
inequalities for norms of projections of an isotropic log-concave vector.
Archive classification: math.PR math.FA math.MG
Mathematics Subject Classification: Primary 52A23, 46B06, 46B09, 60E15
Secondary 15B52, 94B75
Submitted from: radamcz at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.0401
or
http://arXiv.org/abs/1103.0401
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:29:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Embeddability of locally finite
metric spaces into Banach spaces is finitely determined" by Mikhail
I. Ostrovskii.
Abstract: The main purpose of the paper is to prove the following results:
Let $A$ be a locally finite metric space whose finite subsets admit
uniformly
bilipschitz embeddings into a Banach space $X$. Then $A$ admits a
bilipschitz embedding into $X$.
Let $A$ be a locally finite metric space whose finite subsets admit
uniformly
coarse embeddings into a Banach space $X$. Then $A$ admits a coarse
embedding into $X$.
These results generalize previously known results of the same type due to
Brown-Guentner (2005), Baudier (2007), Baudier-Lancien (2008), and the
author (2006, 2009).
One of the main steps in the proof is: each locally finite subset of an
ultraproduct $X^\mathcal{U}$ admits a bilipschitz embedding into $X$. We
explain how this result can be used to prove analogues of the main
results for other classes of embeddings.
Archive classification: math.FA
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.0748
or
http://arXiv.org/abs/1103.0748
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:31:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Auerbach bases and minimal volume
sufficient enlargements" by Mikhail I. Ostrovskii.
Abstract: Let $B_Y$ denote the unit ball of a normed linear space $Y$. A
symmetric, bounded, closed, convex set $A$ in a finite dimensional normed
linear space $X$ is called a {\it sufficient enlargement} for $X$ if,
for an arbitrary isometric embedding of $X$ into a Banach space $Y$,
there exists a linear projection $P:Y\to X$ such that $P(B_Y)\subset
A$. Each finite dimensional normed space has a minimal-volume sufficient
enlargement which is a parallelepiped, some spaces have ``exotic''
minimal-volume sufficient enlargements. The main result of the paper is
a characterization of spaces having ``exotic'' minimal-volume sufficient
enlargements in terms of Auerbach bases.
Archive classification: math.FA
Mathematics Subject Classification: 46B07 (primary), 52A21, 46B15
(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/1103.0997
or
http://arXiv.org/abs/1103.0997
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 Mar 2011 11:33:32 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lushness, numerical index 1 and
the Daugavet property in rearrangement invariant spaces" by Vladimir
Kadets, Miguel Martin, Javier Meri, and Dirk Werner.
Abstract: We show that for spaces with 1-unconditional bases lushness, the
alternative Daugavet property and numerical index~1 are equivalent. In
the class of rearrangement invariant (r.i.)\ sequence spaces the
only examples of spaces with these properties are $c_0$, $\ell_1$ and
$\ell_\infty$. The only lush r.i.\ separable function space on $[0,1]$
is $L_1[0,1]$; the same space is the only r.i.\ separable function space
on $[0,1]$ with the Daugavet property over the reals.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04. Secondary 46E30
Submitted from: werner at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.1282
or
http://arXiv.org/abs/1103.1282
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Enrique A. Sanchez Perez and Dirk Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:35:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The $p$-Daugavet property for
function spaces" by Enrique A. Sanchez Perez and Dirk Werner.
Abstract: A natural extension of the Daugavet property for $p$-convex
Banach function spaces and related classes is analysed. As an application,
we extend the arguments given in the setting of the Daugavet property
to show that no reflexive space falls into this class.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, secondary 46B25
Submitted from: werner at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.1284
or
http://arXiv.org/abs/1103.1284
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tord Sj\"odin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:37:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A note on Gram-Schmidt's algorithm
for a general angle" by Tord Sj\"odin.
Abstract: The Gram-Schmidt algorithm produces a pairwise orthogonal set
from a linearly independent set of vectors in an inner product vector
space V. We give a linear algorithm that constructs vectors with the
same span and which have pairwise the same prescribed angle or distance,
in all cases where this is possible. Finally, we prove an asymptotic
property in the case of an infinite dimensional space V.
Archive classification: math.FA math.GM math.MG
Mathematics Subject Classification: Primary 15 A 03, Secondary 15 A 63,
46 C 05
Remarks: 8 pages
Submitted from: tord.sjodin at math.umu.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.1310
or
http://arXiv.org/abs/1103.1310
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boris Rubin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:41:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Funk, cosine, and sine transforms
on Stiefel and Grassmann manifolds, II" by Boris Rubin.
Abstract: We investigate analytic continuation of the matrix cosine and
sine transforms introduced in Part I and depending on a complex parameter
$\a$. It is shown that the cosine transform corresponding to $\a=0$ is a
constant multiple of the Funk-Radon transform in integral geometry for
a pair of Stiefel (or Grassmann) manifolds. The same case for the sine
transform gives the identity operator. These results and the relevant
composition formula for the cosine transforms were established in Part
I in the sense of distributions. Now we have them pointwise. Some new
problems are formulated.
Archive classification: math.FA
Remarks: 18 pages
Submitted from: borisr at math.lsu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.1161
or
http://arXiv.org/abs/1103.1161
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:43:18 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Random series of trace class
operators" by Gilles Pisier.
Abstract: In this lecture, we present some results on Gaussian (or
Rademacher) random series of trace class operators, mainly due jointly
with F. Lust-Piquard. We will emphasize the probabilistic reformulation of
these results, as well as the open problems suggested by them. We start
by a brief survey of what is known about the problem of characterizing
a.s. convergent (Gaussian or Rademacher) series of random vectors in a
Banach space. The main result presented here is that for certain pairs
of Banach spaces $E,F$ that include Hilbert spaces
(and type 2 spaces with the analytic UMD property), we have $$
R(E\widehat\otimes F) =R(E)\widehat\otimes F + E\widehat\otimes R(F)
$$ where $R(E)$ denotes the space of convergent Rademacher series with
coefficients in $E$ and
$E\widehat\otimes F$ denotes the projective tensor product.
Archive classification: math.FA math.OA math.PR
Mathematics Subject Classification: 46B09
Citation: Proceedings Cuarto CLAPEM Mexico 1990. Contribuciones en
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.2090
or
http://arXiv.org/abs/1103.2090
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:47:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Completely co-bounded Schur
multipliers" by Gilles Pisier.
Abstract: A linear map $u\colon \ E\to F$ between operator spaces
is called completely co-bounded if it is completely bounded as a map
from $E$ to the opposite of $F$. We give several simple results about
completely co-bounded Schur multipliers on $B(\ell_2)$ and the Schatten
class $S_p$. We also consider Herz-Schur multipliers on groups.
Archive classification: math.FA math.OA
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.2108
or
http://arXiv.org/abs/1103.2108
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boaz Klartag and Emanuel Milman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:51:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Centroid bodies and the logarithmic
Laplace transform - A unified approach" by Boaz Klartag and Emanuel
Milman.
Abstract: We unify and slightly improve several bounds on the isotropic
constant of high-dimensional convex bodies; in particular, a linear
dependence on the body's psi-2 constant is obtained. Along the way,
we present some new bounds on the volume of L_p-centroid bodies and yet
another equivalent formulation of Bourgain's hyperplane conjecture. Our
method is a combination of the L_p-centroid body technique of Paouris
and the logarithmic Laplace transform technique of the first named author.
Archive classification: math.FA
Submitted from: klartagb at post.tau.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.2985
or
http://arXiv.org/abs/1103.2985
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej F.K. Kalenda and Jiri Spurny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:53:18 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On a difference between
quantitative weak sequential completeness and the quantitative Schur
property" by Ondrej F.K. Kalenda and Jiri Spurny.
Abstract: We study quantitative versions of the Schur property and weak
sequential completeness, proceeding thus with investigations started by
G. Godefroy, N. Kalton and D. Li and continued by H. Pfitzner and the
authors. We show that the Schur property of $\ell_1$ holds quantitatively
in the strongest possible way and construct an example of a Banach
space which is quantitatively weakly sequentially complete, has the
Schur property but fails the quantitative form of the Schur property.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B25
Remarks: 7 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/1103.2975
or
http://arXiv.org/abs/1103.2975
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dirk Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:54:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Nigel Kalton's work in isometrical
Banach space theory" by Dirk Werner.
Abstract: This paper surveys some of the late Nigel Kalton's contributions
to Banach space theory. The paper is written for the Nigel Kalton Memorial
Website http://mathematics.missouri.edu/kalton/, which is scheduled to
go online in summer 2011.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B03, 46B28
Submitted from: werner at math.fu-berlin.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.3153
or
http://arXiv.org/abs/1103.3153
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Nazim I. Mahmudov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 21 Mar 2011 11:56:10 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Korovkin type theorem for iterates
of certain positive linear operators" by Nazim I. Mahmudov.
Abstract: In this paper we prove that if T:C[0,1]→C[0,1] is a positive
linear operator with T(e₀)=1 and T(e₁)-e₁ does not change the sign,
then the iterates T^{m} converges to some positive linear operator T^{∞}
:C[0,1]→C[0,1] and we derive quantitative estimates in terms of modulii
of smoothness. This result enlarges the class of operators for which the
limit of the iterates can be computed and the quantitative estimates of
iterates can be given.
Archive classification: math.FA
Submitted from: mahmudov2009 at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.2918
or
http://arXiv.org/abs/1103.2918
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Informal analysis seminar at Kent State
From: Dale Alspach <alspach at math.okstate.edu>
Date: Thu, 07 Apr 2011 15:37:17 -0500
To: banach at math.okstate.edu
This is an announcement of an two-day long
informal analysis seminar at Kent State which will be held next Thursday
and Friday, April 14 and 15.
Richard M. Aron
aron at math.kent.edu
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Informal analysis seminar at Kent State (resend)
From: Dale Alspach <alspach at math.okstate.edu>
Date: Thu, 07 Apr 2011 20:00:16 -0500
To: banach at math.okstate.edu
Some information was omitted from the previous post.
This is an announcement of a two-day long
informal analysis seminar at Kent State which will be held next Thursday
and Friday, April 14 and 15.
More information about the schedule of talks is available at
http://www.kent.edu/math/upload/informal-analysis-sem-announcement.pdf
Richard M. Aron
aron at math.kent.edu
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Luong Dang Ky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Apr 2011 21:33:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "New Hardy spaces of Musielak-Orlicz
type and boundedness of sublinear operators" by Luong Dang Ky.
Abstract: We introduce a new class of Hardy spaces
$H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$, called Hardy spaces of
Musielak-Orlicz type, which generalize the Hardy-Orlicz spaces of Janson
and the weighted Hardy spaces of Garc\'ia-Cuerva, Str\"omberg, and
Torchinsky. Here, $\varphi: \mathbb R^n\times [0,\infty)\to [0,\infty)$
is a function such that $\varphi(x,\cdot)$ is an Orlicz function and
$\varphi(\cdot,t)$ is a Muckenhoupt $A_\infty$ weight. A function $f$
belongs to $H^{\varphi(\cdot,\cdot)}(\mathbb R^n)$ if and only if
its maximal function $f^*$ is so that $x\mapsto \varphi(x,|f^*(x)|)$
is integrable. Such a space arises naturally for instance in the
description of the product of functions in $H^1(\mathbb R^n)$ and
$BMO(\mathbb R^n)$ respectively (see \cite{BGK}). We characterize
these spaces via the grand maximal function and establish their atomic
decomposition. We characterize also their dual spaces. The class of
pointwise multipliers for $BMO(\mathbb R^n)$ characterized by Nakai
and Yabuta can be seen as the dual of $L^1(\mathbb R^n)+ H^{\rm
log}(\mathbb R^n)$ where $ H^{\rm log}(\mathbb R^n)$ is the Hardy
space of Musielak-Orlicz type related to the Musielak-Orlicz function
$\theta(x,t)=\displaystyle\frac{t}{\log(e+|x|)+ \log(e+t)}$. Furthermore,
under additional assumption on $\varphi(\cdot,\cdot)$ we prove that if
$T$ is a sublinear operator and maps all atoms into uniformly bounded
elements of a quasi-Banach space $\mathcal B$, then $T$ uniquely extends
to a bounded sublinear operator from $H^{\varphi(\cdot,\cdot)}(\mathbb
R^n)$ to $\mathcal B$. These results are new even for the classical
Hardy-Orlicz spaces on $\mathbb R^n$.
Archive classification: math.CA math.FA
Submitted from: dangky at math.cnrs.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.3757
or
http://arXiv.org/abs/1103.3757
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Guo TieXin and Zeng XiaoLin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Apr 2011 21:37:13 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "An $L^{0}({\cal F},R)-$valued
function's intermediate value theorem and its applications to random
uniform convexity" by Guo TieXin and Zeng XiaoLin.
Abstract: Let $(\Omega,{\cal F},P)$ be a probability space and
$L^{0}({\cal F},R)$ the algebra of equivalence classes of real-valued
random variables on $(\Omega,{\cal F},P)$. When $L^{0}({\cal F},R)$
is endowed with the topology of convergence in probability, we prove
an intermediate value theorem for a continuous local function from
$L^{0}({\cal F},R)$ to $L^{0}({\cal F},R)$. As applications of this
theorem, we first give several useful expressions for modulus of
random convexity, then we prove that a complete random normed module
$(S,\|\cdot\|)$ is random uniformly convex iff $L^{p}(S)$ is uniformly
convex for each fixed positive number $p$ such that $1<p<+\infty$.
Archive classification: math.FA
Mathematics Subject Classification: 46A22, 46B20, 46E30
Remarks: 14pages
Submitted from: xlinzeng at ss.buaa.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.3775
or
http://arXiv.org/abs/1103.3775
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Oscar Blasco, Geraldo Botelho, Daniel
Pellegrino and Pilar Rueda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Apr 2011 21:39:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the interplay between different
summability properties of multilinear mappings" by Oscar Blasco,
Geraldo Botelho, Daniel Pellegrino and Pilar Rueda.
Abstract: In this paper we establish profitable connections between
different summability properties of multilinear mappings on Banach
spaces, namely, multilinear mappings that are absolutely summing,
almost summing, weakly summing and Cohen summing. For example, we give
techniques to extend coincidence results from linear, bilinear and, in
general, n-linear mappings to m-linear mappings for m larger than n. We
do so by exploring the relationships between the summability properties
of an n-linear mapping with those of its associated k-linear mappings,
1 <= k < n. We also provide an optimal generalization of recent results
concerning inclusion theorems for absolutely summing multilinear mappings.
Archive classification: math.FA
Remarks: 27 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.4040
or
http://arXiv.org/abs/1103.4040
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christina Brech and Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Apr 2011 21:44:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On universal spaces for the
class of Banach spaces whose dual balls are uniform Eberlein compacts"
by Christina Brech and Piotr Koszmider.
Abstract: For k being the first uncountable cardinal w_1 or k being
the cardinality of the continuum c, we prove that it is consistent
that there is no Banach space of density k in which it is possible to
isomorphically embed every Banach space of the same density which has
a uniformly G\^ateaux differentiable renorming or, equivalently, whose
dual unit ball with the weak* topology is a subspace of a Hilbert space
(a uniform Eberlein compact space). This complements a consequence of
results of M. Bell and of M. Fabian, G. Godefroy, V. Zizler that assuming
the continuum hypothesis, there is a universal space for all Banach
spaces of density k=c=w_1 which have a uniformly G\^ateaux differentiable
renorming. Our result implies, in particular, that \beta N-N may not
map continuously onto a compact subset of a Hilbert space with the weak
topology of density k=w_1 or k=c and that a C(K) space for some uniform
Eberlein compact space K may not embed isomorphically into l_\infty/c_0.
Archive classification: math.FA math.GN math.LO
Mathematics Subject Classification: Primary 46B26, Secondary 03E35, 46B03
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.4259
or
http://arXiv.org/abs/1103.4259
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Michael Dore and Olga Maleva
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 11 Apr 2011 21:48:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A universal differentiability
set in Banach spaces with separable dual" by Michael Dore and Olga Maleva.
Abstract: We show that any non-zero Banach space with a separable dual
contains a totally disconnected, closed and bounded subset S of Hausdorff
dimension 1 such that every Lipschitz function on the space is Fr\'echet
differentiable somewhere in S.
Archive classification: math.FA
Remarks: 41 pages, 1 figure
Submitted from: michael.j.dore at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.5094
or
http://arXiv.org/abs/1103.5094
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] International Conference AMAT 2012// New Book
From: "George A Anastassiou (ganastss)" <ganastss at memphis.edu>
Date: Thu, 28 Apr 2011 14:25:51 -0500
To: "George A Anastassiou (ganastss)" <ganastss at memphis.edu>
Dear Colleague Hi!
Two announcements you may be concerned:
1) Please find complete information about the International Conference
on "Applied Mathematics and Approximation Theory 2012", to be held
in Ankara, Turkey, May 17-19, 2012.
So for all you need please visit:
http://amat2012.etu.edu.tr/
For whatever you need please contact the organizer
Professor Oktay Duman at
oduman at etu.edu.tr<mailto:oduman at etu.edu.tr>
please do not contact George Anastassiou.
2) May be your Library or you can order the new SPRINGER
book-monograph
by G. Anastassiou and O. Duman
"Statistical Approximation Theory",
(nothing to do with Statistics), all necessary information attached.
Thank You for Your patience.
I hope I see you in Ankara next year.
Sincerely Yours
George A. Anastassiou,Ph.D
DOCTOR HONORIS CAUSA
Professor of Mathematics
Department of Mathematical Sciences
The University of Memphis,Memphis,TN 38152,USA
Editor-In-Chief JoCAAA, JCAAM,JAFA ;World Sci.Publ.Book Series:
Concrete & Applicable Math.
Springer Consultant-Editor in computational math books
Birkhauser Consultant Editor in A.M.Sci.
CRC-A.M. Advisor
NOVA MATH books ADVISOR
ganastss at memphis.edu
http://www.eudoxuspress.com
http://www.msci.memphis.edu/~ganastss/jocaaa
http://www.msci.memphis.edu/~ganastss/jcaam
http://www.msci.memphis.edu/~ganastss/jafa
tel:(INT 001)- 901-678-3144 office
901-751-3553 home
901-678-2482 secr.
Fax: 901-678-2480
Associate Editor in:
J.Communications in Applied Analysis,
Inter.J.Applied Math.,Inter.J.Diff.Eq.&Appl.,CUBO,
J.Advances in non-linear Variational Inequalities,
e-J.of Inequalities in Pure and Applied Math.,
Anals U.Oradea-Fasciola Mathematica,
Journal of Inequalities and Applications,
Inter.J.of Pure&Appl.Math.,MIA,
Inter.J.of Computational and Numerical Analysis with Appl.
President of world Soc.for study & promotion of
Ancient Greek Mathematics.
Honorary Editor Australian Journal of Mathematical Analysis and Appl.
Panamerican Mathematical Journal
Eudoxus Press,LLC Pres.
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_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
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Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Felix Cabello, Jesus M. F.
Castillo, Manuel Gonzalez, and Yolanda Moreno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 13:53:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On separably injective Banach
spaces" by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo, Manuel
Gonzalez, and Yolanda Moreno.
Abstract: In this paper we deal with two weaker forms of injectivity
which turn out to have a rich structure behind: separable injectivity and
universal separable injectivity. We show several structural and stability
properties of these classes of Banach spaces. We provide natural examples
of (universally) separably injective spaces, including $\mathcal L_\infty$
ultraproducts built over countably incomplete ultrafilters, in spite
of the fact that these ultraproducts are never injective. We obtain two
fundamental characterizations of universally separably injective spaces:
a) A Banach space $E$ is universally separably injective if and only if
every separable subspace is contained in a copy of $\ell_\infty$ inside
$E$. b) A Banach space $E$ is universally separably injective if and only
if for every separable space $S$ one has $\Ext(\ell_\infty/S, E)=0$. The
final Section of the paper focuses on special properties of $1$-separably
injective spaces. Lindenstrauss\ obtained in the middle sixties a result
that can be understood as a proof that, under the continuum hypothesis,
$1$-separably injective spaces are $1$-universally separably injective;
he left open the question in {\sf ZFC}. We construct a consistent example
of a Banach space of type $C(K)$ which is $1$-separably injective but
not $1$-universally separably injective.
Archive classification: math.FA
Mathematics Subject Classification: 46A22, 46B04, 46B08, 46A22, 46B04,
46B08, 46B26
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.6064
or
http://arXiv.org/abs/1103.6064
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Aviles, Felix Cabello, Jesus M. F.
Castillo, Manuel Gonzalez, and Yolanda Moreno
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 13:55:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Banach spaces of universal
disposition" by Antonio Aviles, Felix Cabello, Jesus M. F. Castillo,
Manuel Gonzalez, and Yolanda Moreno.
Abstract: In this paper we present a method to obtain Banach spaces
of universal and almost-universal disposition with respect to a given
class $\mathfrak M$ of normed spaces. The method produces, among other,
the Gurari\u{\i} space $\mathcal G$ (the only separable Banach space
of almost-universal disposition with respect to the class $\mathfrak
F$ of finite dimensional spaces), or the Kubis space $\mathcal K$
(under {\sf CH}, the only Banach space with the density character the
continuum which is of universal disposition with respect to the class
$\mathfrak S$ of separable spaces). We moreover show that $\mathcal K$
is not isomorphic to a subspace of any $C(K)$-space -- which provides
a partial answer to the injective space problem-- and that --under {\sf
CH}-- it is isomorphic to an ultrapower of the Gurari\u{\i} space.
We study further properties of spaces of universal disposition:
separable injectivity, partially automorphic character and uniqueness
properties.
Archive classification: math.FA
Mathematics Subject Classification: 46A22, 46B04, 46B08, 46B26
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.6065
or
http://arXiv.org/abs/1103.6065
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mark Braverman, Konstantin Makarychev, Yury
Makarychev, and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 13:56:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Grothendieck constant is
strictly smaller than Krivine's bound" by Mark Braverman, Konstantin
Makarychev, Yury Makarychev, and Assaf Naor.
Abstract: We prove that $K_G<\frac{\pi}{2\log\left(1+\sqrt{2}\right)}$,
where $K_G$ is the Grothendieck constant.
Archive classification: math.FA
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.6161
or
http://arXiv.org/abs/1103.6161
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Nayar and Tomasz Tkocz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 13:59:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On a Loomnis-Whitney type
inequality for permutationally invariant unconditional convex bodies"
by Piotr Nayar and Tomasz Tkocz.
Abstract: For a permutationally invariant unconditional convex body K
in R^n we define a finite sequence (K_j), j = 1, ..., n of projections
of the body K to the space spanned by first j vectors of the standard
basis of R^n. We prove that the sequence of volumes (|K_1|, ..., |K_n|)
is log-concave.
Archive classification: math.FA
Mathematics Subject Classification: 52A20 (Primary), 52A40 (Secondary)
Remarks: 5 pages
Submitted from: t.tkocz at students.mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.6232
or
http://arXiv.org/abs/1103.6232
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Witold Marciszewski and Grzegorz Plebanek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 14:00:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On measures on Rosenthal compacta"
by Witold Marciszewski and Grzegorz Plebanek.
Abstract: We show that if K is Rosenthal compact which can be represented
by functions with countably many discontinuities then every Radon
measure on K is countably determined. We also present an alternative
proof of the result stating that every Radon measure on an arbitrary
Rosenthal compactum is of countable type. Our approach is based on
some caliber-type properties of measures, parameterized by separable
metrizable spaces.
Archive classification: math.FA
Mathematics Subject Classification: 28C15, 46A50 (Primary) 28A60, 54C35
(Secondary)
Remarks: 14 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/1104.2639
or
http://arXiv.org/abs/1104.2639
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denis Potapov, Fedor Sukochev, and Quanhua
Xu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 14:02:03 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the vector-valued
Littlewood-Paley-Rubio de Francia inequality" by Denis Potapov, Fedor
Sukochev, and Quanhua Xu.
Abstract: The paper studies Banach spaces satisfying the
Littlewood-Paley-Rubio de Francia property LPR_p, 2 \leq p < \infty. The
paper shows that every Banach lattice whose 2-concavification is a UMD
Banach lattice has this property. The paper also shows that every space
having LPR_q also has LPR_p with q \leq p < \infty.
Archive classification: math.FA
Submitted from: d.potapov at unsw.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.2671
or
http://arXiv.org/abs/1104.2671
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Peter Elbau
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 14:04:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sequential lower semi-continuity
of non-local functionals" by Peter Elbau.
Abstract: We give a necessary and sufficient condition for non-local
functionals on vector-valued Lebesgue spaces to be weakly sequentially
lower semi-continuous. Here a non-local functional shall have the form
of a double integral of a density which depends on the function values
at two different points.
The characterisation we get is essentially that the density has to
be convex in one variable if we integrate over the other one with an
arbitrary test function in it. Moreover, we show that this condition
is in the case of non-local functionals on real-valued Lebesgue spaces
(up to some equivalence in the density) equivalent to the separate
convexity of the density.
Archive classification: math.FA
Mathematics Subject Classification: 49J05, 49J45
Remarks: 23 pages
Submitted from: elbau at math.ethz.ch
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.2686
or
http://arXiv.org/abs/1104.2686
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Lajara, A. Pallares and S. Troyanski
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 14:11:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Moduli of convexity and smoothness
of reflexive subspaces of L^1" by S. Lajara, A. Pallares and S. Troyanski.
Abstract: We show that for any probability measure \mu there exists
an equivalent norm on the space L^1(\mu) whose restriction to each
reflexive subspace is uniformly smooth and uniformly convex, with modulus
of convexity of power type 2. This renorming provides also an estimate
for the corresponding modulus of smoothness of such subspaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B10, 46B20, 46B25
Submitted from: apall at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.2802
or
http://arXiv.org/abs/1104.2802
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hulya Duru, Arkady Kitover, and Mehmet
Orhon
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 14:13:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Multiplication operators on
vector-valued function spaces" by Hulya Duru, Arkady Kitover, and
Mehmet Orhon.
Abstract: Let $E$ be a Banach function space on a probability measure
space $(\Omega ,\Sigma,\mu).$ Let $X$ be a Banach space and $E(X)$
be the associated K\"{o}the-Bochner space. An operator on $E(X)$ is
called a multiplication operator if it is given by multiplication by a
function in $L^{\infty}(\mu).$ In the main result of this paper, we show
that an operator $T$ on $E(X)$ is a multiplication operator if and only
if $T$ commutes with $L^{\infty}(\mu)$ and leaves invariant the cyclic
subspaces generated by the constant vector-valued functions in $E(X).$ As
a corollary we show that this is equivalent to $T$ satisfying a functional
equation considered by Calabuig, Rodr\'{i}guez, S\'{a}nchez-P\'{e}rez in
[3].
Archive classification: math.FA
Mathematics Subject Classification: 47B38 (Primary) 46G10, 46B42, 46H25
(Secondary)
Submitted from: mo at unh.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.2806
or
http://arXiv.org/abs/1104.2806
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 14:21:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$\alpha$-minimal Banach spaces"
by Christian Rosendal.
Abstract: A Banach space with a Schauder basis is said to be
$\alpha$-minimal for some countable ordinal $\alpha$ if, for any two
block subspaces, the Bourgain embeddability index of one into the other
is at least $\alpha$. We prove a dichotomy that characterises when a
Banach space has an $\alpha$-minimal subspace, which contributes to the
ongoing project, initiated by W. T. Gowers, of classifying separable
Banach spaces by identifying characteristic subspaces.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 46B03, 03E15
Submitted from: rosendal at math.uic.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.3543
or
http://arXiv.org/abs/1104.3543
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Almut Burchard and Marc Fortier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 29 Apr 2011 14:23:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Convergence of random
polarziations" by Almut Burchard and Marc Fortier.
Abstract: We derive conditions under which random sequences of
polarizations converge almost surely to the symmetric decreasing
rearrangement. The parameters for the polarizations are independent
random variables whose distributions may be far from uniform. The proof
of convergence hinges on an estimate for the expected distance from
the limit that also yields a bound on the rate of convergence. In the
special case of i.i.d. sequences, we obtain almost sure convergence
even for polarizations chosen at random from small sets. The precise
characterization of convergent sequences remains an open problem. These
statements about polarization allow us to improve the existing
convergence results for Steiner symmetrization. In particular, we show
that full rotational symmetry can be achieved by alternating Steiner
symmetrization along directions that satisfy an explicit non-degeneracy
condition. Finally, we construct examples for dense sequences of
directions such that the corresponding Steiner symmetrizations do not
converge.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 60D05 (26D15, 28A75, 52A52)
Remarks: 30 pages, 6 figures
Submitted from: almut at math.toronto.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.4103
or
http://arXiv.org/abs/1104.4103
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Valerio Capraro, Tobias Fritz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 May 2011 13:57:00 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the axiomatization of convex
subsets of Banach spaces" by Valerio Capraro, Tobias Fritz.
Abstract: We prove that any convex-like structure in the sense of
Nate Brown is affinely and isometrically isomorphic to a closed convex
subset of a Banach space. This answers an open question of Brown. As an
intermediate step, we identify Brown's algebraic axioms as equivalent
to certain well-known axioms of abstract convexity.
Archive classification: math.MG math.FA math.OA
Mathematics Subject Classification: Primary 52A01, Secondary 46L36
Remarks: 8 pages, 1 figure
Submitted from: tobias.fritz at icfo.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.1270
or
http://arXiv.org/abs/1105.1270
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Majid Gazor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 May 2011 13:11:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Condensation rank of injective
Banach spaces" by Majid Gazor.
Abstract: The condensation rank associates any topological space with
a unique ordinal number. In this paper we prove that the condensation
rank of any infinite dimensional injective Banach space is equal to or
greater than the first uncountable ordinal number.
Archive classification: math.FA
Mathematics Subject Classification: 46B25, 03E10, 54A05, 28A05
Submitted from: m.gazor.iut at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.4896
or
http://arXiv.org/abs/1104.4896
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, 13 May 2011 13:08:52 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Banach spaces without minimal
subspaces - examples" by Valentin Ferenczi and Christian Rosendal.
Abstract: We analyse several examples of separable Banach spaces, some of
them new, and relate them to several dichotomies obtained in the previous
paper spaces without minimal subspaces of the dichotomies they fall. This
paper may be seen as a more empirical continuation of is on the study
of examples for the new classes of Banach spaces considered in that work.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 03E15
Remarks: 29 pages, to appear in Annales de l
Submitted from: ferenczi at ccr.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1104.4724
or
http://arXiv.org/abs/1104.4724
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jose L. Gamez-Merino, Gustavo A.
Munoz-Fernandez, Daniel Pellegrino and Juan B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 May 2011 13:59:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bounded and unbounded
polynomials and multilinear forms: Characterizing continuity" by Jose
L. Gamez-Merino, Gustavo A. Munoz-Fernandez, Daniel Pellegrino and Juan
B. Seoane-Sepulveda.
Abstract: In this paper we prove a characterization of continuity for
polynomials on a normed space. Namely, we prove that a polynomial is
continuous if and only if it maps compact sets into compact sets. We also
provide a partial answer to the question as to whether a polynomial is
continuous if and only if it transforms connected sets into connected
sets. These results motivate the natural question as to how many
non-continuous polynomials there are on an infinite dimensional normed
space. A problem on the \emph{lineability} of the sets of non-continuous
polynomials and multilinear mappings on infinite dimensional normed
spaces is answered.
Archive classification: math.FA
Remarks: 8 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.1737
or
http://arXiv.org/abs/1105.1737
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Elisabeth M. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 May 2011 13:14:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Renyi Divergence and $L_p$-affine
surface area for convex bodies" by Elisabeth M. Werner.
Abstract: We show that the fundamental objects of the
$L_p$-Brunn-Minkowski theory, namely the $L_p$-affine surface areas
for a convex body, are closely related to information theory: they are
exponentials of R\'enyi divergences of the cone measures of a convex
body and its polar.
We give geometric interpretations for all R\'enyi divergences
$D_\alpha$, not just for the previously treated special case of relative
entropy which is the case $\alpha =1$. Now, no symmetry assumptions are
needed and, if at all, only very weak regularity assumptions are required.
Previously, the relative entropies appeared only after performing second
order expansions of certain expressions. Now already first order
expansions makes them appear. Thus, in the new approach we detect
``faster" details about the boundary of a convex body.
Archive classification: math.FA
Mathematics Subject Classification: 52A20, 53A15
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/1105.1124
or
http://arXiv.org/abs/1105.1124
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Rafal Gorak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 13 May 2011 13:12:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Perturbations of isometries
between Banach spaces" by Rafal Gorak.
Abstract: We prove a very general theorem concerning the estimation
of the expression \mbox{$\|T(\frac{a+b}{2}) - \frac{Ta+Tb}{2}\|$}
for different kinds of maps $T$ satisfying some general perurbated
isometry condition. It can be seen as a quantitative generalization of the
classical Mazur-Ulam theorem. The estimates improve the existing ones for
bi-Lipschitz maps. As a consequence we also obtain a very simple proof of
the result of Gevirtz which answers the Hyers-Ulam problem and we prove
a non-linear generalization of the Banach-Stone theorem which improves
the results of Jarosz and more recent results of Dutrieux and Kalton.
Archive classification: math.FA
Mathematics Subject Classification: 46E40, 46B20
Submitted from: R.Gorak at mini.pw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.0854
or
http://arXiv.org/abs/1105.0854
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by A. Koldobsky, G. Paouris and M.
Zymonopoulou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:19:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isomorphic properties of
intersection bodies" by A. Koldobsky, G. Paouris and M. Zymonopoulou.
Abstract: We study isomorphic properties of two generalizations of
intersection bodies, the class of k-intersection bodies and the class
of generalized k-intersection bodies. We also show that the Banach-Mazur
distance of the k-intersection body of a convex body, when it exists and
it is convex, with the Euclidean ball, is bounded by a constant depending
only on k, generalizing a well-known result of Hensley and Borell. We
conclude by giving some volumetric estimates for k-intersection bodies.
Archive classification: math.FA
Submitted from: marisa.zym at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.2629
or
http://arXiv.org/abs/1105.2629
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:20:44 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Examples of k-iterated spreading
models" by Spiros A. Argyros and Pavlos Motakis.
Abstract: It is shown that for every $k\in\mathbb{N}$ and every spreading
sequence $\{e_n\}_{n\in\mathbb{N}}$ that generates a uniformly convex
Banach space $E$, there exists a uniformly convex Banach space $X_{k+1}$
admitting $\{e_n\}_{n\in\mathbb{N}}$ as a $k+1$-iterated spreading model,
but not as a $k$-iterated one.
Archive classification: math.FA
Remarks: 16 pages, no figures
Submitted from: pmotakis at central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.2714
or
http://arXiv.org/abs/1105.2714
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S.A. Argyros, V. Kanellopoulos and K. Tyros
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:22:23 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Finite order spreading models"
by S.A. Argyros, V. Kanellopoulos and K. Tyros.
Abstract: Extending the classical notion of the spreading model,
the $k$-spreading models of a Banach space are introduced, for every
$k\in\mathbb{N}$. The definition, which is based on the $k$-sequences and
plegma families, reveals a new class of spreading sequences associated
to a Banach space. Most of the results of the classical theory are
stated and proved in the higher order setting. Moreover, new phenomena
like the universality of the class of the 2-spreading models of $c_0$
and the composition property are established. As consequence, a problem
concerning the structure of the $k$-iterated spreading models is solved.
Archive classification: math.FA
Remarks: 41 pages, no figures
Submitted from: chcost at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.2732
or
http://arXiv.org/abs/1105.2732
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cleon Barroso, Geraldo Botelho, Vinicius V.
Favaro and Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:28:47 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spaceability for the weak form of
Peano's theorem and vector-valued sequence spaces" by Cleon Barroso,
Geraldo Botelho, Vinicius V. Favaro and Daniel Pellegrino.
Abstract: Two new applications of a technique for spaceability are
given in this paper. For the first time this technique is used in the
investigation of the algebraic genericity property of the weak form of
Peano's theorem on the existence of solutions of the ODE $u'=f(u)$ on
$c_0$. The space of all continuous vector fields $f$ on $c_0$ is proved
to contain a closed $\bf c$-dimensional subspace formed by fields $f$ for
which -- except for the null field -- the weak form of Peano's theorem
fails to be true. The second application generalizes known results on
the existence of closed $\bf c$-dimensional subspaces inside certain
subsets of $\ell_p(X)$-spaces, $0 < p < \infty$, to the existence of
closed subspaces of maximal dimension inside such subsets.
Archive classification: math.FA
Remarks: 10 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.2845
or
http://arXiv.org/abs/1105.2845
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Justin Jenkinson and Elisabeth Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:30:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Relative entropies for convex
bodies" by Justin Jenkinson and Elisabeth Werner.
Abstract: We introduce a new class of (not necessarily convex) bodies
and show, among other things, that these bodies provide yet another
link between convex geometric analysis and information theory. Namely,
they give geometric interpretations of the relative entropy of the cone
measures of a convex body and its polar and related quantities.
Such interpretations were first given by Paouris and Werner for
symmetric convex bodies in the context of the $L_p$-centroid
bodies. There, the relative entropies appear after performing second
order expansions of certain expressions. Now, no symmetry assumptions are
needed. Moreover, using the new bodies, already first order expansions
make the relative entropies appear. Thus, these bodies detect ``faster"
details of the boundary of a convex body than the $L_p$-centroid bodies.
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/1105.2846
or
http://arXiv.org/abs/1105.2846
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Oleg Reinov and Qaisar Latif
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:32:02 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Grothendieck-Lidskii theorem
for subspaces and factor spaces of L_p-spaces" by Oleg Reinov and
Qaisar Latif.
Abstract: In 1955, A. Grothendieck has shown that if the linear operator
$T$ in a Banach subspace of an $L_\infty$-space is $2/3$-nuclear
then the trace of $T$ is well defined and is equal to the sum of all
eigenvalues $\{\mu_k(T)\}$ of $T.$ V.B. Lidski\v{\i} , in 1959, proved his
famous theorem on the coincidence of the trace of the $S_1$-operator in
$L_2(\nu)$ with its spectral trace $\sum_{k=1}^\infty \mu_k(T).$ We show
that for $p\in[1,\infty]$ and $s\in (0,1]$ with $1/s=1+|1/2-1/p|,$ and for
every $s$-nuclear operator $T$ in every subspace of any $L_p(\nu)$-space
the trace of $T$ is well defined and equals the sum of all eigenvalues
of $T.$
Archive classification: math.FA
Mathematics Subject Classification: 47B06
Remarks: LaTeX2e, 5 pages
Submitted from: orein51 at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.2914
or
http://arXiv.org/abs/1105.2914
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Qinggang Ren
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:33:40 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Coarse embedding into uniformly
convex Banach space" by Qinggang Ren.
Abstract: In this paper, we study the coarse embedding into Banach
space. We proved that under certain conditions, the property of embedding
into Banach space can be preserved under taking the union the metric
spaces. For a group $G$ strongly relative hyperbolic to a subgroup $H$,
we proved that if $H$ admits a coarse embedding into a uniformly convex
Banach space, so is $B(n)=\{g\in G|\abs{g}_{S\cup\mathscr{H}}\leq n\}$.
Archive classification: math.MG math.FA
Remarks: 14 pages
Submitted from: qinggang.ren at hw4.ecs.kyoto-u.ac.jp
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.3263
or
http://arXiv.org/abs/1105.3263
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pavel Ludvik and Jiri Spurny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:35:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Descriptive properties of elements
of biduals of Banach spaces" by Pavel Ludvik and Jiri Spurny.
Abstract: If $E$ is a Banach space, any element $x^{**}$ in its bidual
$E^{**}$ is an affine function on the dual unit ball $B_{E^*}$ that
might possess variety of descriptive properties with respect to the weak*
topology. We prove several results showing that descriptive properties of
$x^{**}$ are quite often determined by the behaviour of $x^{**}$ on the
set of extreme points of $B_{E^*}$, generalizing thus results of J. Saint
Raymond and F. Jellett. We also prove several results on relation between
Baire classes and intrinsic Baire classes of $L_1$-preduals which were
introduced by S.A. Argyros, G. Godefroy and H.P. Rosenthal. Also, several
examples witnessing natural limits of our positive results are presented.
Archive classification: math.FA
Mathematics Subject Classification: 46B99, 46A55, 26A21
Submitted from: spurny at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.3413
or
http://arXiv.org/abs/1105.3413
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Thomas Schlumprecht
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:36:28 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the closed subideals of
$L(\ell_p\oplus\ell_q)$" by Thomas Schlumprecht.
Abstract: In this paper we first review the known results about the closed
subideals of the space of bounded operator on $\ell_p\oplus \ell_q$,
$1<p<q<\infty$, and then construct several new ones.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 47L20. Secondary: 47B10,
47B37
Remarks: To appear in Operators and Matrices
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/1105.3610
or
http://arXiv.org/abs/1105.3610
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Carando and Daniel Galicer
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 23 May 2011 15:37:38 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Five basic lemmas for symmetric
tensor products of normed spaces" by Daniel Carando and Daniel Galicer.
Abstract: We give the symmetric version of five lemmas which are
essential for the theory of tensor products (and norms). These are:
the approximation, extension, embedding, density and local technique
lemmas. Some application of these tools to the metric theory of symmetric
tensor products and to the theory of polynomials ideals are given.
Archive classification: math.FA
Mathematics Subject Classification: 46M05, 46G25, 47L22
Remarks: 24 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/1105.3746
or
http://arXiv.org/abs/1105.3746
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Longyun Ding and Zhi Yin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 3 Jun 2011 15:37:53 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Borel equivalence relations
between \ell_1 and \ell_p" by Longyun Ding and Zhi Yin.
Abstract: In this paper, we show that, for each $p>1$, there are continuum
many Borel equivalence relations between $\Bbb R^\omega/\ell_1$ and $\Bbb
R^\omega/\ell_p$ ordered by $\le_B$ which are pairwise Borel incomparable.
Archive classification: math.LO math.FA
Mathematics Subject Classification: 03E15, 46F45
Remarks: 7 pages, submitted
Submitted from: dingly at nankai.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.4492
or
http://arXiv.org/abs/1105.4492
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Niemiec
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 3 Jun 2011 15:39:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Central points and measures and
dense subsets of compact metric spaces" by Piotr Niemiec.
Abstract: For every nonempty compact convex subset $K$ of a normed linear
space a (unique) point $c_K \in K$, called the generalized Chebyshev
center, is distinguished. It is shown that $c_K$ is a common fixed
point for the isometry group of the metric space $K$. With use of the
generalized Chebyshev centers, the central measure $\mu_X$ of an arbitrary
compact metric space $X$ is defined. For a large class of compact metric
spaces, including the interval $[0,1]$ and all compact metric groups,
another `central' measure is distinguished, which turns out to coincide
with the Lebesgue measure and the Haar one for the interval and a compact
metric group, respectively. An idea of distinguishing infinitely many
points forming a dense subset of an arbitrary compact metric space is
also presented.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46S30, 47H10, Secondary
46A55, 46B50
Remarks: 13 pages
Submitted from: piotr.niemiec at uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.5706
or
http://arXiv.org/abs/1105.5706
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Petr Hajek and Jarno Talponen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 3 Jun 2011 15:40:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Smooth approximations of norms
in separable Banach spaces" by Petr Hajek and Jarno Talponen.
Abstract: Let X be a separable real Banach space having a k-times
continuously Fr\'{e}chet differentiable (i.e. C^k-smooth) norm where
k=1,...,\infty. We show that any equivalent norm on X can be approximated
uniformly on bounded sets by C^k-smooth norms.
Archive classification: math.FA math.AG
Mathematics Subject Classification: Primary 46B03, 46T20, Secondary
47J07, 14P20
Remarks: 10 pages
Submitted from: talponen at cc.hut.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.6046
or
http://arXiv.org/abs/1105.6046
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. Botelho, V. V. Favaro, D. Pellegrino
and J. B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 3 Jun 2011 15:42:51 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "$L_{p}[0,1] \setminus
\bigcup\limits_{q>p} L_{q}[0,1]$ is spaceable for every $p>0$" by
G. Botelho, V. V. Favaro, D. Pellegrino and J. B. Seoane-Sepulveda.
Abstract: In this short note we prove the result stated in the title;
that is, for every $p>0$ there exists an infinite dimensional closed
linear subspace of $L_{p}[0,1]$ every nonzero element of which does not
belong to $\bigcup\limits_{q>p} L_{q}[0,1]$. This answers in the positive
a question raised in 2010 by R. M. Aron on the spaceability of the above
sets (for both, the Banach and quasi-Banach cases). We also complete
some recent results from \cite{BDFP} for subsets of sequence spaces.
Archive classification: math.FA
Remarks: 3 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.0309
or
http://arXiv.org/abs/1106.0309
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Philipp Hoffmann and Michael Mackey
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 3 Jun 2011 15:44:26 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the second parameter of an $(m,
p)$-Isometry" by Philipp Hoffmann and Michael Mackey.
Abstract: A bounded linear operator $T$ on a Banach space $X$ is called
an $(m, p)$-isometry if it satisfies the equation $\sum_{k=0}^{m}(-1)^{k}
{m \choose k}\|T^{k}x\|^{p} = 0$, for all $x \in X$. In the first part of
this paper we study the structure which underlies the second parameter
of $(m, p)$-isometric operators. More precisely, we concentrate on
the question of determining conditions on $q \neq p$ for which an
$(m, p)$-isometry can be a $(\mu, q)$-isometry for some $\mu$. In
the second part we extend the definition of $(m, p)$-isometry, to
include $p=\infty$. We then study basic properties of these $(m,
\infty)$-isometries.
Archive classification: math.FA
Submitted from: philipp.hoffmann at ucdconnect.ie
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.0339
or
http://arXiv.org/abs/1106.0339
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Rosendal
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 3 Jun 2011 15:46:01 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Characterising subspaces of
Banach spaces with a Schauder basis having the shift property" by
Christian Rosendal.
Abstract: We give an intrinsic characterisation of the separable
reflexive Banach spaces that embed into separable reflexive spaces
with an unconditional basis all of whose normalised block sequences with
the same growth rate are equivalent. This uses methods of E. Odell and
T. Schlumprecht.
Archive classification: math.FA
Mathematics Subject Classification: 46B03
Submitted from: rosendal at math.uic.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.0472
or
http://arXiv.org/abs/1106.0472
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Lasse Leskela and Matti Vihola
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:20:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Stochastic order characterization
of uniform integrability and tightness" by Lasse Leskela and Matti Vihola.
Abstract: We show that a family of random variables is uniformly
integrable if and only if it is stochastically bounded in the increasing
convex order by an integrable random variable. This result is complemented
by proving analogous statements for the strong stochastic order and
for power-integrable dominating random variables. Especially, we show
that whenever a family of random variables is stochastically bounded
by a p-integrable random variable for some p>1, there is no distinction
between the strong order and the increasing convex order. These results
also yield new characterizations of relative compactness in Wasserstein
and Prohorov metrics.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 60E15, 60B10, 60F25
Remarks: 14 pages, 1 figure
Submitted from: lasse.leskela at iki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.0607
or
http://arXiv.org/abs/1106.0607
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mark Rudelson and Shuheng Zhou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:25:02 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Reconstruction from anisotropic
random measurements" by Mark Rudelson and Shuheng Zhou.
Abstract: Random matrices are widely used in sparse recovery problems,
and the relevant properties of matrices with i.i.d. entries are
well understood. The current paper discusses the recently introduced
Restricted Eigenvalue (RE) condition, which is among the most general
assumptions on the matrix, guaranteeing recovery. We prove a reduction
principle showing that the RE condition can be guaranteed by checking the
restricted isometry on a certain family of low-dimensional subspaces. This
principle allows us to establish the RE condition for several broad
classes of random matrices with dependent entries, including random
matrices with subgaussian rows and non-trivial covariance structure,
as well as matrices with independent rows, and uniformly bounded entries.
Archive classification: math.ST cs.IT math.FA math.IT stat.TH
Report Number: Technical Report 522, University of Michigan, Department
of Statistics
Remarks: 30 Pages
Submitted from: szhou at cs.cmu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.1151
or
http://arXiv.org/abs/1106.1151
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jarno Talponen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:26:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Convex-transitivity of Banach
algebras via ideals" by Jarno Talponen.
Abstract: We investigate a method for producing concrete convex-transitive
Banach spaces. The gist of the method is in getting rid of dissymmetries
of a given space by taking a carefully chosen quotient. The spaces of
interest here are typically Banach algebras and their ideals. We also
investigate the convex-transitivity of ultraproducts and tensor products
of Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 47L20, 46Mxx, 47L10
Remarks: 18 pages
Submitted from: talponen at cc.hut.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.1292
or
http://arXiv.org/abs/1106.1292
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Taras Banakh and Ivan Hetman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:27:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A hidden characterization of
polyhedral convex sets" by Taras Banakh and Ivan Hetman.
Abstract: We prove that a closed convex subset $C$ of a complete linear
metric space $X$ is polyhedral in its closed linear hull if and only if no
infinite subset $A\subset X\backslash C$ can be hidden behind $C$ in the
sense $[x,y]\cap C\not = \emptyset$ for any distinct points $x,y\in A$.
Archive classification: math.FA math.CO
Mathematics Subject Classification: 46A55, 52B05, 52A07, 52A37
Remarks: 8 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.2227
or
http://arXiv.org/abs/1106.2227
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Guillaume Aubrun, Stanislaw J. Szarek and
Deping Ye
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:29:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Entanglement thresholds for random
induced states" by Guillaume Aubrun, Stanislaw J. Szarek and Deping Ye.
Abstract: For a random quantum state on $H=C^d \otimes C^d$ obtained
by partial tracing a random pure state on $H \otimes C^s$, we consider
the whether it is typically separable or typically entangled. We show
that a threshold occurs when the environment dimension $s$ is of order
roughly $d^3$. More precisely, when $s \leq cd^3$, such a random state is
entangled with very large probability, while when $s \geq Cd^3 \log^2 d$,
it is separable with very large probability (here $C,c>0$ are appropriate
effectively computable universal constants). Our proofs rely on random
matrices, classical convexity, high-dimensional probability and geometry
of Banach spaces. Our methods work also for multipartite systems and for
"unbalanced" systems such as $C^{d} \otimes C^{d'}$, $d \neq d' $.
Archive classification: quant-ph math.FA math.PR
Report Number: Mittag-Leffler-2010fall
Remarks: 29 pages
Submitted from: szarek at cwru.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.2264
or
http://arXiv.org/abs/1106.2264
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ranjana Jain and Ajay Kumar
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:31:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Operator space projective tensor
product: Embedding into second dual and ideal structure" by Ranjana
Jain and Ajay Kumar.
Abstract: We prove that for operator spaces $V$ and $W$, the operator
space $V^{**}\otimes_h W^{**}$ can be completely isometrically
embedded into $(V\otimes_h W)^{**}$, $\otimes_h$ being the Haagerup
tensor product. It is also shown that, for exact operator spaces $V$
and $W$, a jointly completely bounded bilinear form on $V\times W$
can be extended uniquely to a separately $w^*$-continuous jointly
completely bounded bilinear form on $ V^{**}\times W^{**}$. This paves
the way to obtain a canonical embedding of $V^{**}\widehat{\otimes}
W^{**}$ into $(V\widehat{\otimes} W)^{**}$ with a continuous inverse,
where $\widehat{\otimes}$ is the operator space projective tensor
product. Further, for $C^*$-algebras $A$ and $B$, we study the (closed)
ideal structure of $A\widehat{\otimes}B$, which, in particular, determines
the lattice of closed ideals of $B(H)\widehat{\otimes} B(H)$ completely.
Archive classification: math.FA
Mathematics Subject Classification: 46L06, 46L07, 47L25
Remarks: 13 pages
Submitted from: rjain.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.2644
or
http://arXiv.org/abs/1106.2644
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:32:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A C(K) Banach space which does
not have the Schroeder-Bernstein property" by Piotr Koszmider.
Abstract: We construct a totally disconnected compact Hausdorff space
N which has clopen subsets M included in L included in N such that N is
homeomorphic to M and hence C(N) is isometric as a Banach space to C(M)
but C(N) is not isomorphic to C(L). This gives two nonisomorphic Banach
spaces of the form C(K) which are isomorphic to complemented subspaces
of each other (even in the above strong isometric sense), providing
a solution to the Schroeder-Bernstein problem for Banach spaces of the
form C(K). N is obtained as a particular compactification of the pairwise
disjoint union of a sequence of Ks for which C(K)s have few operators.
Archive classification: math.FA math.GN
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.2917
or
http://arXiv.org/abs/1106.2917
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Koszmider
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:33:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On large indecomposable Banach
spaces" by Piotr Koszmider.
Abstract: Hereditarily indecomposable Banach spaces may have density
at most continuum (Plichko-Yost, Argyros-Tolias). In this paper we
show that this cannot be proved for indecomposable Banach spaces. We
provide the first example of an indecomposable Banach space of density
two to continuum. The space exists consistently, is of the form C(K)
and it has few operators in the sense that any bounded linear operator
T on C(K) satisfies T(f)=gf+S(f) for every f in C(K), where g is in C(K)
and S is weakly compact (strictly singular).
Archive classification: math.FA math.GN math.LO
Submitted from: piotr.math at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.2916
or
http://arXiv.org/abs/1106.2916
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Nikhil Srivastava and Roman Vershynin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:35:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Covariance estimation for
distributions with 2+ε moments" by Nikhil Srivastava and Roman Vershynin.
Abstract: We study the minimal sample size N=N(n) that suffices to
estimate the covariance matrix of an n-dimensional distribution by the
sample covariance matrix in the operator norm, and with an arbitrary fixed
accuracy. We establish the optimal bound N = O(n) for every distribution
whose k-dimensional marginals have uniformly bounded 2+\epsilon moments
outside the sphere of radius O(\sqrt{k}). In the specific case of
log-concave distributions, this result provides an alternative approach
to the Kannan-Lovasz-Simonovits problem, which was recently solved
by Adamczak, Litvak, Pajor and Tomczak-Jaegermann. Moreover, a lower
estimate on the covariance matrix holds under a weaker assumption --
uniformly bounded 2+\epsilon moments of one-dimensional marginals. Our
argument proceeds by randomizing the spectral sparsification technique
of Batson, Spielman and Srivastava. The spectral edges of the sample
covariance matrix are controlled via the Stieltjes transform evaluated
at carefully chosen random points.
Archive classification: math.PR math.ST
Submitted from: nikhils at math.ias.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.2775
or
http://arXiv.org/abs/1106.2775
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Justin Tatch Moore
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:36:31 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Amenability and Ramsey Theory"
by Justin Tatch Moore.
Abstract: The purpose of this article is to connect the notion of the
amenability of a discrete group with a new form of structural Ramsey
theory. The Ramsey theoretic reformulation of amenability constitutes
a considerable weakening of the F\o lner criterion. As a bi-product,
it will be shown that in any non amenable group G, there is a subset E
of G such that no finitely additive probability measure on G measures
all translates of E equally.
Archive classification: math.GR math.CO math.FA math.LO
Mathematics Subject Classification: 05D10, 05C55, 20F38, 20F65, 43A07
Remarks: 13 pages. Comments welcome
Submitted from: justin at math.cornell.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.3127
or
http://arXiv.org/abs/1106.3127
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by B. F. Svaiter
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:37:34 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Gauge functions for convex cones"
by B. F. Svaiter.
Abstract: We analyze a class of sublinear functionals which characterize
the interior and the exterior of a convex cone in a normed linear space.
Archive classification: math.FA math.OC
Mathematics Subject Classification: 46B99, 46N10
Submitted from: benar at impa.br
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.3342
or
http://arXiv.org/abs/1106.3342
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Antonio Falco and Anthony Nouy
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:39:24 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Proper generalized decomposition
for nonlinear convex problems in tensor Banach spaces" by Antonio Falco
and Anthony Nouy.
Abstract: Tensor-based methods are receiving a growing interest in
scientific computing for the numerical solution of problems defined
in high dimensional tensor product spaces. A family of methods called
Proper Generalized Decompositions methods have been recently introduced
for the a priori construction of tensor approximations of the solution
of such problems. In this paper, we give a mathematical analysis of
a family of progressive and updated Proper Generalized Decompositions
for a particular class of problems associated with the minimization of
a convex functional over a reflexive tensor Banach space.
Archive classification: math.NA math.FA math.OC
Mathematics Subject Classification: 65K10, 49M29
Submitted from: afalco at uch.ceu.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.4424
or
http://arXiv.org/abs/1106.4424
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Asuman Guven Aksoy and Grzegorz Lewicki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 27 Jun 2011 12:41:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Limit theorems for numerical index"
by Asuman Guven Aksoy and Grzegorz Lewicki.
Abstract: We improve upon on a limit theorem for numerical index for
large classes of Banach spaces including vector valued $\ell_p$-spaces
and $\ell_p$-sums of Banach spaces where\\ $1\leq p \leq \infty$. We first
prove $ n_1( X) = \displaystyle \lim_m n_1( X_m)$ for a modified numerical
index $n_1(\, .\, )$. Later, we establish if a norm on $X$ satisfies
the local characterization condition, then $n(X) = \displaystyle\lim_m
n(X_m).$ We also present an example of a Banach space where the local
characterization condition is satisfied.
Archive classification: math.FA math.OA
Submitted from: aaksoy at cmc.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.4822
or
http://arXiv.org/abs/1106.4822
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: Mon, 27 Jun 2011 12:43:04 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On isometry groups and maximal
symmetry" by Valentin Ferenczi and Christian Rosendal.
Abstract: We study problems of maximal symmetry in Banach spaces. This
is done by providing an analysis of the structure of small subgroups of
the general linear group GL(X), where X is a separable reflexive Banach
space. In particular, we provide the first known example of a Banach
space X without any equivalent maximal norm, or equivalently such that
GL(X) contains no maximal bounded subgroup. Moreover, this space X may
be chosen to be super-reflexive.
Archive classification: math.FA math.LO
Mathematics Subject Classification: Primary: 22F50, 46B03,
46B04. Secondary: 03E15
Submitted from: rosendal at math.uic.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.5020
or
http://arXiv.org/abs/1106.5020
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS 2011
From: Bill Johnson <johnson at math.tamu.edu>
Date: Fri, 1 Jul 2011 11:37:50 -0500 (CDT)
To: banach at math.okstate.edu
1st ANNOUNCEMENT OF SUMIRFAS 2011
The Informal Regional Functional Analysis Seminar
July 29 - 31
Texas A&M University, College Station
Schedule: Talks for SUMIRFAS will be posted on the Workshop in Analysis
and Probability page, URL
http://www.math.tamu.edu/conferences/linanalysis/
The first talk will be in the early afternoon on Friday and the Seminar
concludes by lunch time on Sunday. All talks will be in Blocker 169. The
Blocker Building is on Ireland St. just south of University Dr. on the
Texas A&M campus:
http://www.math.tamu.edu/contact/blocker.html.
Coffee and refreshments will be available in Blocker 148.
Speakers at SUMIRFAS 2011 include
Gregory Berkolaiko, Nodal count of eigenfunctions and stability of nodal
partitions
Gilles Godefroy, The complexity of the isomorphism relation on the set of
subspaces of a given Banach space: is it possible to improve Gowers'
dichotomy?
Ciprian Foias, "End of the road" problems in Operator Theory
Bill Helton, Free semi-definite programming and its limitations
Boris Kashin, N-term approximations and some corrections theorem
Constanze Liaw, Dilations and rank one perturbations
Eve Oja, The weak metric approximation property of Banach spaces
Mihai Putinar, Quillen's phenomenon on pseudoconvex boundaries
Jean Roydor, A non-commutative Amir-Cambern Theorem
Vladimir Temlyakov, Lebesgue-type inequalities for greedy approximation
with respect to redundant systems
Steve Dilworth, Daniel Freeman, Denka Kuzarova, Edward Odell (co-chair),
and Thomas Schlumprecht (co-chair) are organizing a Concentration Week on
"Greedy Algorithms in Banach spaces and Compressed Sensing" for the week
of July 18-22. When encoding or reconstructing a vector using an iterative
algorithm, a natural
approach is to take the best or biggest approximation at each iteration.
Such techniques are referred to as greedy algorithms. The theory of
compressed sensing is concerned with encoding and reconstructing vectors
which are sparsely represented with respect to a given basis. Kevin Ford
will present a series of talks on deterministic construction of matrices
with the restrictive isometry property. There will be a second series of
talks devoted to greedy algorithms and bases. The home page for this
Concentration Week is at
http://www.math.utexas.edu/users/freeman/greedy11/index.html
Florent Baudier (chair), Bill Johnson, Piotr Nowak, and Bunyamin Sari are
organizing a Concentration Week on "Non-Linear Geometry of Banach Spaces,
Geometric Group Theory, and Differentiability" for the week of August 1-5.
The program will include an introductory course by Mark Sapir on coarse
embeddings and their applications to geometric group theory, and a series
of lectures by Gilles Godefroy on the recent work of the late Nigel Kalton
on the coarse classification of Banach spaces. The home page for this
Concentration Week is at
http://www.math.tamu.edu/~pnowak/index/cw.html
We expect to be able to cover housing for most participants from support
the
National Science Foundation has provided for the Workshop. When you ask
Cara to book your room, please tell her if you are requesting support.
Minorities, women, graduate students, and young researchers are especially
encouraged to apply.
For logistical support, including requests for support, contact Cara
Barton <cara at math.tamu.edu>. For more information on the Workshop itself,
contact William Johnson <johnson at math.tamu.edu>, David Larson
<larson at math.tamu.edu>, Gilles Pisier <pisier at math.tamu.edu>, or Joel
Zinn <jzinn at math.tamu.edu>.
For information about the Concentration Week on "Non-Linear Geometry of
Banach Spaces, Geometric Group Theory, and Differentiability", contact
Florent Baudier <florent at math.tamu.edu>.
For information about the Concentration Week on "Greedy Algorithms in
Banach spaces and Compressed Sensing", contact Edward Odell
<odell at mail.ma.utexas.edu> or Thomas Schlumprecht <schlump at math.tamu.edu>.
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jesus M.F. Castillo, Ricardo Garcia, and Jesus Suarez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 7 Jul 2011 15:23:37 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Extension and lifting of operators
and polynomials" by Jesus M.F. Castillo, Ricardo Garcia, and Jesus Suarez.
Abstract: We study the problem of extension and lifting of operators
belonging to certain operator ideals, as well as that of their
associated polynomials and holomorphic functions. Our results provide
a characterization of $\mathcal{L}_1$ and $\mathcal{L}_{\infty}$-spaces
that includes and extends those of Lindenstrauss-Rosenthal \cite{LR} using
compact operators and Gonz\'{a}lez-Guti\'{e}rrez \cite{GG} using compact
polynomials. We display several examples to show the difference between
extending and lifting compact (resp. weakly compact, unconditionally
convergent, separable and Rosenthal) operators to operators of the same
type. Finally, we show the previous results in a homological perspective,
which helps the interested reader to understand the motivations and
nature of the results presented.
Archive classification: math.FA
Remarks: to appear in Mediterranean J. of Mathematics
Submitted from: castillo at unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.5088
or
http://arXiv.org/abs/1106.5088
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by J.M.F. Castillo, A. Defant, R. Garcia, D. Perez-Garcia, and
J. Suarez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 7 Jul 2011 15:25:29 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Local complementation and the
extension of bilinear mappings" by J.M.F. Castillo, A. Defant, R. Garcia,
D. Perez-Garcia, and J. Suarez.
Abstract: We study different aspects of the connections between local
theory of Banach spaces and the problem of the extension of bilinear forms
from subspaces of Banach spaces. Among other results, we prove that if
$X$ is not a Hilbert space then one may find a subspace of $X$ for which
there is no Aron-Berner extension. We also obtain that the extension of
bilinear forms from all the subspaces of a given $X$ forces such $X$ to
contain no uniform copies of $\ell_p^n$ for $p\in[1,2)$. In particular,
$X$ must have type $2-\varepsilon$ for every $\varepsilon>0$. Also, we
show that the bilinear version of the Lindenstrauss-Pe\l czy\'{n}ski and
Johnson-Zippin theorems fail. We will then consider the notion of locally
$\alpha$-complemented subspace for a reasonable tensor norm $\alpha$,
and study the connections between $\alpha$-local complementation and
the extendability of $\alpha^*$ -integral operators.
Archive classification: math.FA
Remarks: to appear in Mathematical Proceedings of the Cambridge
Philosophical
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.5089
or
http://arXiv.org/abs/1106.5089
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Arseniy Akopyan and Roman Karasev
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 7 Jul 2011 15:26:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Kadets type theorems for partitions
of a convex body" by Arseniy Akopyan and Roman Karasev.
Abstract: For convex partitions of a convex body $B$ we prove that we
can put a homothetic copy of $B$ into each set of the partition so that
the sum of homothety coefficients is $\ge 1$. In the plane the partition
may be arbitrary, while in higher dimensions we need certain restrictions
on the partition.
Archive classification: math.CO math.FA
Mathematics Subject Classification: 52C15, 52C17, 52A40, 52A21
Submitted from: r_n_karasev at mail.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1106.5635
or
http://arXiv.org/abs/1106.5635
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Omer Friedland and Olivier Guedon
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 7 Jul 2011 15:28:11 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sparsity and non-Euclidean
embeddings" by Omer Friedland and Olivier Guedon.
Abstract: We present a relation between sparsity and non-Euclidean
isomorphic embeddings. We introduce a general restricted isomorphism
property and show how it enables to construct embeddings of $\ell_p^n$, $p
> 0$, into various type of Banach or quasi-Banach spaces. In particular,
for $0 <r < p<2$ with $r \le 1$, we construct a family of operators
that embed $\ell_p^n$ into $\ell_r^{(1+\eta)n}$, with optimal polynomial
bounds in $\eta >0$.
Archive classification: math.FA
Submitted from: omerfrie at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.0992
or
http://arXiv.org/abs/1107.0992
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] SUMIRFAS Schedule
From: Dale Alspach <alspach at math.okstate.edu>
Date: Thu, 21 Jul 2011 12:39:24 -0500
To: banach at math.okstate.edu
SCHEDULE FOR SUMIRFAS 2010
The Informal Regional
Functional Analysis Seminar
July 29 - 31, 2011
Texas A&M University, College Station
Talks for SUMIRFAS will also be posted on the Workshop in Analysis and
Probability page:
http://www.math.tamu.edu/conferences/linanalysis/
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.tamu.edu/map/building/overview/BLOC.html
Coffee and refreshments will be available in Blocker 148.
The usual SUMIRFAS dinner will be on July 30. It will be a BBQ at the home
of Jan and
Bill Johnson.
Florent Baudier (chair), Bill Johnson, Piotr Nowak, and Bunyamin Sari are
organizing a
Concentration Week on Non-Linear Geometry of Banach Spaces,
Geometric Group Theory,
and Differentiability for the week of August 1-5. The program
will include an introductory
course by Mark Sapir on coarse embeddings and their applications to
geometric group theory,
and a series of lectures by Gilles Godefroy on the recent work of the late
Nigel Kalton on
the coarse classification of Banach spaces. The home page for this
Concentration Week is at
http://www.math.tamu.edu/ pnowak/index/cw.html
We expect to be able to cover housing for most participants from support
the National
Science Foundation has provided for the Workshop. When you ask Cara to book
your room,
please tell her if you are requesting support. Minorities, women, graduate
students, and
young researchers are especially encouraged to apply.
For logistical support, please contact Cara Barton, cara at math.tamu.edu. For
more infor-
mation on the Workshop itself, please contact William Johnson,
johnson at math.tamu.edu,
David Larson, larson at math.tamu.edu, Gilles Pisier, pisier at math.tamu.edu, or
Joel Zinn,
jzinn at math.tamu.edu.
Schedule for SUMIRFAS 2011
Friday, July 29 Blocker 166
1:30-1:55 Coffee & refreshments, Blocker 148
1:55-2:00 Greeting
2:00-3:00 Gregory Berkolaiko, Nodal count of
eigenfunctions and stability of nodal partitions
3:10-3:50 Constanze Liaw, Dilations and rank one perturbations
3:50-4:15 Coffee & refreshments, Blocker 148
4:15-5:15 Mihai Putinar, Quillens phenomenon
on pseudoconvex boundaries
Saturday, July 30 Blocker 166
9:00-9:20 Coffee & refreshments, Blocker 148
9:50-10:50 Boris Kashin, N -term approximations and some corrections theorems
11:00-12:00 Eve Oja, The weak metric approximation property of Banach spaces
12:00-2:00 Lunch
2:00-3:00 Vladimir Temlyakov, Lebesgue-type inequalities
for greedy approximation with respect to redundant systems
3:10-3:50 Jean Roydor, A non-commutative Amir-Cambern Theorem
3:50-4:10 Coffee & refreshments, Blocker 148
4:10-5:10 Gilles Godefroy, The complexity of the isomorphism relation
on the set of subspaces of a given Banach space: is it possible to improve
Gowers dichotomy?
6:30 BBQ & swimming at Jan & Bill Johnson's house,
1306 Deacon Dr., College Station,
979.696.2812, 979.450.2812. Please tell Cara,
cara at math.tamu.edu
if you (and spouse or companion, if applicable) will attend.
Sunday, July 31 Blocker 166
9:30-9:50 Coffee & refreshments, Blocker 148
9:50-10:50 Ciprian Foias, End of the road problems in Operator Theory
11:00-12:00 Bill Helton, Free semi-definite programming
and its limitations
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Subject: [Banach] Functional Analysis Methods in Quantum Information. EMS
Mathematical Weekend. October 7-9. Bilbao. Spain
From: David Perez-Garcia <dperez at mat.ucm.es>
Date: Fri, 22 Jul 2011 12:15:30 +0200
To: banach at math.okstate.edu
Dear colleague,
As part of the commemorations of its centennial, the Royal Spanish Society
of Mathematics (RSME) is organizing jointly with the European Mathematical
Society (EMS) a Mathematical Weekend that will be held in Bilbao from
October 7 to 9, 2011. As is usual in the EMS Mathematical Weekends, the
meeting will begin on Friday afternoon and will end on Sunday at lunch
time.
All mathematicians, from Europe and elsewhere, are warmly invited to
participate.
As in previous editions of the EMS Mathematical Weekends, there will be
several special sessions where some of the most prominent researchers in
their fields will give a talk. In this edition, these are the four topics
that have been selected for the special sessions: Groups and
Representations, Symplectic Geometry, PDEs in Mechanics and Physics, and
Functional Analysis Methods in Quantum Information.
Related to the fourth topic, which presents the modern connections
between
Functional Analysis and Information Theory, Computer Science, Probability
and Geometry, there will be a plenary talk and 6 invited contributions. The
fact that the EMS and the RSME have included these new connections of
Functional Analysis as a 'hot topic' illustrates their relevance for future
research. It is hence a wonderful occasion, specially for young
researchers,
to assist and have contact with some leading researchers in the area.
We hope to see you in Bilbao this fall.
Jesus Bastero and David Perez-Garcia
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Registration Open: Functional Analysis Methods in Quantum
Information. EMS Mathematical Weekend. October 7-9. Bilbao. Spain
From: David Perez-Garcia <dperez at mat.ucm.es>
Date: Tue, 26 Jul 2011 11:26:26 +0200
To: banach at math.okstate.edu
Dear colleague,
The registration is already open for the Mathematical Weekend jointly
organized by the Royal Spanish Society of Mathematics and the European
Mathematical Society. You can register and find more information about the
meeting in http://www.ehu.es/emsweekend/
Important data about the meeting:
Dates: October 7-9, 2011
Venue: The Bizkaia Aretoa, Bilbao, Spain. Very close to the famous
Guggenheim Museum.
Special sessions: Groups and Representations, Symplectic Geometry, PDEs in
Mechanics and Physics, Functional Analysis Methods in Quantum Information.
See you there!
Jesus Bastero and David Perez-Garcia
(organizers of the session Functional Analysis Methods in Quantum
Information)
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr W. Nowak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 10:53:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Poincar\'e inequalities and
rigidity for actions on Banach spaces" by Piotr W. Nowak.
Abstract: The aim of this paper is to extend the framework of the
spectral method for proving property (T) to the class of reflexive
Banach spaces and present conditions implying that every affine isometric
action of a given group $G$ on a reflexive Banach space $X$ has a fixed
point. This last property is a strong version of Kazhdan's property (T)
and is equivalent to the fact that $H^1(G,\pi)=0$ for every isometric
representation $\pi$ of $G$ on $X$. We give examples of groups for which
every affine isometric action on an $L_p$ space has a fixed point for
certain $p>2$, and present several applications. In particular, we give
a lower bound on the conformal dimension of the boundary of a hyperbolic
group in the Gromov density model.
Archive classification: math.GR math.FA math.OA
Submitted from: pnowak at math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.1896
or
http://arXiv.org/abs/1107.1896
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Silvia Lassalle and Pablo Turco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 10:54:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On p-compact mappings and
p-approximation" by Silvia Lassalle and Pablo Turco.
Abstract: The notion of $p$-compact sets arises naturally from
Grothendieck's characterization of compact sets as those contained
in the convex hull of a norm null sequence. The definition, due to
Sinha and Karn (2002), leads to the concepts of $p$-approximation
property and $p$-compact operators, which form a ideal with its ideal
norm $\kappa_p$. This paper examines the interaction between the
$p$-approximation property and the space of holomorphic functions.
Here, the $p$-compact analytic functions play a crucial role. In order
to understand this type of functions we define a $p$-compact radius of
convergence which allow us to give a characterization of the functions
in the class. We show that $p$-compact holomorphic functions behave more
like nuclear than compact maps. We use the $\epsilon$-product, defined
by Schwartz, to characterize the $p$-approximation property of a Banach
space in terms of $p$-compact homogeneous polynomials and also in terms
of $p$-compact holomorphic functions with range on the space. Finally,
we show that $p$-compact holomorphic functions fit in the framework of
holomorphy types which allows us to inspect the $\kappa_p$-approximation
property. Along these notes we solve several questions posed by Aron,
Maestre and Rueda.
Archive classification: math.FA
Mathematics Subject Classification: 46G20, 46B28
Remarks: 31 pages
Submitted from: pabloaturco at yahoo.com.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.1670
or
http://arXiv.org/abs/1107.1670
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Wilczek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 10:56:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Under the Continuum Hypothesis
all nonreflexive Banach space ultrapowers are primary" by Piotr Wilczek.
Abstract: In this note a large class of primary Banach spaces is
characterized. Namely, it will be demonstrated that under the Continuum
Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive
Banach space is always primary. Consequently, any infinite dimensional
nonsuperreflexive Banach space can be isometrically embedded into its
primary ultrapowers.
Archive classification: math.LO math.FA
Mathematics Subject Classification: 46B08, 46B20, 46B25
Remarks: 7 pages
Submitted from: edwil at mail.icpnet.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.1692
or
http://arXiv.org/abs/1107.1692
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Piotr Wilczek
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 10:58:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Some representation theorem for
nonreflexive Banach space ultrapowers under the Continuum Hypothesis"
by Piotr Wilczek.
Abstract: In this paper it will be shown that assuming the Continuum
Hypothesis (CH) every nonreflexive Banach space ultrapower is
isometrically isomorphic to the space of continuous, bounded and
real-valued functions on the Parovicenko space. This Representation
Theorem will be helpful in proving some facts from geometry and topology
of nonreflexive Banach space ultrapowers.
Archive classification: math.LO math.FA
Mathematics Subject Classification: 46B08, 46B20, 46B25
Remarks: 12 pages
Submitted from: edwil at mail.icpnet.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.1693
or
http://arXiv.org/abs/1107.1693
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Nir Lev and Alexander Olevskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 11:00:59 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Wiener's 'closure of translates'
problem and Piatetski-Shapiro's uniqueness phenomenon" by Nir Lev and
Alexander Olevskii.
Abstract: Wiener characterized the cyclic vectors (with respect to
translations) in $l^p(Z)$ and $L^p(R)$, $p=1,2$, in terms of the zero set
of the Fourier transform. He conjectured that a similar characterization
should be true for $1<p<2$. Our main result contradicts this conjecture.
Archive classification: math.CA math.FA
Mathematics Subject Classification: 42A63 (Primary) 43A45, 47A16
(Secondary)
Citation: Annals of Mathematics 174 (2011), 519-541
Submitted from: levnir at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0908.0447
or
http://arXiv.org/abs/0908.0447
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by David Alonso-Gutierrez, Jesus Bastero and
Julio Bernues
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 12:26:08 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Factoring Sobolev inequalities
through classes of functions" by David Alonso-Gutierrez, Jesus Bastero
and Julio Bernues.
Abstract: We recall two approaches to recent improvements of the classical
Sobolev inequality. The first one follows the point of view of Real
Analysis, while the second one relies on tools from Convex Geometry. In
this paper we prove a (sharp) connection between them.
Archive classification: math.FA
Mathematics Subject Classification: 46E35, 46E30, 26D10, 52A40
Submitted from: bernues at unizar.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.2139
or
http://arXiv.org/abs/1107.2139
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sonja Cox and Mark Veraar
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 12:38:42 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Vector-valued decoupling and the
Burkholder-Davis-Gundy inequality" by Sonja Cox and Mark Veraar.
Abstract: Let X be a Banach space. We prove p-independence of the
one-sided decoupling inequality for X-valued tangent martingales as
introduced by Kwapien and Woyczynski. It is known that a Banach space X
satisfies the two-sided decoupling inequality if and only if X is a UMD
Banach space. The one-sided decoupling inequality is a weaker property,
including e.g. the space L^1. We provide information on the optimal
constants for various spaces, and give a upper estimate of order p in
general. In the second part of our paper we derive Burkholder-Davis-Gundy
type estimates for p-th moments, p in (0,infty), of X-valued stochastic
integrals, provided X is a UMD Banach space or a space in which the
one-sided decoupling inequality holds.
Archive classification: math.FA
Remarks: To appear in the Illinois Journal of Mathematics
Submitted from: sonja.cox at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.2218
or
http://arXiv.org/abs/1107.2218
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Denka Kutzarova, Antonis Manoussakis, and
Anna Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 12:40:15 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Isomorphisms and strictly
singular operators in mixed Tsirelson spaces" by Denka Kutzarova,
Antonis Manoussakis, and Anna Pelczar-Barwacz.
Abstract: We study the family of isomorphisms and strictly singular
operators in mixed Tsirelson spaces and their modified versions
setting. We show sequential minimality of modified mixed Tsirelson spaces
$T_M[(\mc{S}_n,\theta_n)]$ satisfying some regularity conditions and
present results on existence of strictly singular non-compact operators on
subspaces of mixed Tsirelson spaces defined by the families $(\mc{A}_n)_n$
and $(\mc{S}_n)_n$.
Archive classification: math.FA
Remarks: 29 pages, no figures
Submitted from: amanousakis at isc.tuc.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.2810
or
http://arXiv.org/abs/1107.2810
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eliran Avni
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 12:41:22 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Calderon couples of p-convexified
Banach lattices" by Eliran Avni.
Abstract: We deal with the question of whether or not the p-convexified
couple (X_0^{(p)},X_1^{(p)}) is a Calderon couple under the assumption
that (X_0,X_1) is a Calderon couple of Banach lattices on some measure
space. In this preliminary version of the paper we find that the answer
is affirmative in the simple case where X_0 and X_1 are sequence spaces
and an additional “positivity” assumption is imposed regarding
(X_0,X_1). We also prove a quantitative version of the result with
appropriate norm estimates. In future versions of this paper we plan to
deal with other and more general cases of these results.
Archive classification: math.FA
Mathematics Subject Classification: 46B70, 46E30
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/1107.3238
or
http://arXiv.org/abs/1107.3238
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grigoris Paouris and Elisabeth M. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 23 Aug 2011 12:42:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the approximation of a polytope
by its dual $L_{p}$-centroid bodies" by Grigoris Paouris and Elisabeth
M. Werner.
Abstract: We show that the rate of convergence on the approximation of
volumes of a convex symmetric polytope P in R^n by its dual L_{p$-centroid
bodies is independent of the geometry of P. In particular we show that
if P has volume 1,
lim_{p\rightarrow \infty} \frac{p}{\log{p}} \left(
\frac{|Z_{p}^{\circ}(P)|}{|P^{\circ}|} -1 \right) = n^{2} .
We provide an application to the approximation of polytopes by uniformly
convex sets.
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/1107.3683
or
http://arXiv.org/abs/1107.3683
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Mathematics Lecturer position at University of Houston -
Victoria
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 24 Aug 2011 20:14:17 -0500
To: banach at math.okstate.edu
The School of Arts and Sciences at the University of Houston -
Victoria (UHV) invites applications for a Mathematics lecturer position
starting in the Spring of 2012.
We seek applicants preferably in the area of functional analysis,
Banach Space Theory, Fixed Point theory. The starting date of the
appointment is somewhat flexible, and we may accept applicants who are
about to defend their PhD dissertation. The expected duties are mainly
teaching four freshman courses per semester (Fall and Spring) and do
service as well. The appointment is initially budgeted for one year,
but is expected to last longer, renewed anually.
Applicants should submit a letter of application, AMS cover sheet,
CV, and have three letters of evaluation sent, preferably by email to
teixeirar at uhv.edu. Applications received by October 15,
2011 will receive full consideration; applications will be accepted
until the position is filled.
UHV is a university with almost 5,000 students, located in Texas, 2
hours from major cities like Houston, Austin, San Antonio, Corpus Christi,
and 3 hours from College Station. Most of the classes will have 25
or less students. Victoria is a city with almost 100 thousand people,
with little of everything. We have applied people working in Computer
Sciences, Biology and Statistics, and we are planning on strengthening
the abstract Mathematics.
UHV is committed to diversity and is an affirmative action, equal
opportunity employer. Applications from women or minorities are
especially encouraged.
- -----------------------------------------------
Ricardo Verotti O. Teixeira
School of Arts & Science
University of Houston-Victoria
http://www.ma.utexas.edu/users/rteixeira
<http://www.ma.utexas.edu/users/rteixeira>
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Radoslaw Adamczak, Rafal Latala, Alexander
E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Aug 2011 15:27:17 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Chevet type inequality and norms
of submatrices" by Radoslaw Adamczak, Rafal Latala, Alexander E. Litvak,
Alain Pajor, and Nicole Tomczak-Jaegermann.
Abstract: We prove a Chevet type inequality which gives an upper bound
for the norm of an isotropic log-concave unconditional random matrix
in terms of expectation of the supremum of ``symmetric exponential"
processes compared to the Gaussian ones in the Chevet inequality. This
is used to give sharp upper estimate for a quantity $\Gamma_{k,m}$ that
controls uniformly the Euclidean operator norm of the sub-matrices with
$k$ rows and $m$ columns of an isotropic log-concave unconditional random
matrix. We apply these estimates to give a sharp bound for the Restricted
Isometry Constant of a random matrix with independent log-concave
unconditional rows. We show also that our Chevet type inequality does
not extend to general isotropic log-concave random matrices.
Archive classification: math.PR math.FA math.MG
Mathematics Subject Classification: Primary 52A23, 46B06, 46B09, 60E15
Secondary 15B52, 94B75
Submitted from: radamcz at mimuw.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.4066
or
http://arXiv.org/abs/1107.4066
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Apostolos Giannopoulos, Grigoris Paouris,
and Beatrice-Helen Vritsiou
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Aug 2011 15:28:44 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A remark on the slicing problem"
by Apostolos Giannopoulos, Grigoris Paouris, and Beatrice-Helen Vritsiou.
Abstract: The purpose of this article is to describe a reduction of the
slicing problem to the study of the parameter I_1(K,Z_q^o(K))=\int_K
||< : ,x> ||_{L_q(K)}dx. We show that an upper bound of the form
I_1(K,Z_q^o(K))\leq C_1q^s\sqrt{n}L_K^2, with 1/2\leq s\leq 1, leads to
the estimate L_n\leq \frac{C_2\sqrt[4]{n}log(n)} {q^{(1-s)/2}}, where
L_n:= max {L_K : K is an isotropic convex body in R^n}.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A23, 46B06, 52A40
Remarks: 24 pages
Submitted from: bevritsi at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.4527
or
http://arXiv.org/abs/1107.4527
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by G. A. Munoz-Fernandez, D. Pellegrino and J.
B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Aug 2011 15:30:34 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Estimates for the asymptotic
behavior of the constants in the Bohnenblust--Hille inequality" by
G. A. Munoz-Fernandez, D. Pellegrino and J. B. Seoane-Sepulveda.
Abstract: A classical inequality due to
H.F. Bohnenblust and E. Hille states that for every
positive integer $n$ there is a constant $C_{n}>0$ so that
$$\left(\sum\limits_{i_{1},\dots,i_{n}=1}^{N}\left\vert U(e_{i_{^{1}}},
\dots ,e_{i_{n}})\right\vert^{\frac{2n}{n+1}}\right)^{\frac{n+1}{2n}}\leq
C_{n}\left\Vert U\right\Vert$$ for every
positive integer $N$ and every $n$-linear mapping
$U:\ell_{\infty}^{N}\times\cdots\times\ell_{\infty}^{N}\rightarrow\mathbb{C}$.
The original estimates for those constants from Bohnenblust and Hille are
$$C_{n}=n^{\frac{n+1}{2n}}2^{\frac{n-1}{2}}.$$ In this note we present
explicit formulae for quite better constants, and calculate the asymptotic
behavior of these estimates, completing recent results of the second
and third authors. For example, we show that, if $C_{\mathbb{R},n}$
and $C_{\mathbb{C},n}$ denote (respectively) these estimates for
the real and complex Bohnenblust--Hille inequality then, for every
even positive integer $n$, $$\frac{C_{\mathbb{R},n}}{\sqrt{\pi}}
= \frac{C_{\mathbb{C},n}}{\sqrt{2}} = 2^{\frac{n+2}{8}}\cdot r_n$$
for a certain sequence $\{r_n\}$ which we estimate numerically to
belong to the interval $(1,3/2)$ (the case $n$ odd is similar).
Simultaneously, assuming that $\{r_n\}$ is in fact convergent,
we also conclude that $$\displaystyle \lim_{n \rightarrow \infty}
\frac{C_{\mathbb{R},n}}{C_{\mathbb{R},n-1}} = \displaystyle \lim_{n
\rightarrow \infty} \frac{C_{\mathbb{C},n}}{C_{\mathbb{C},n-1}}=
2^{\frac{1}{8}}.$$
Archive classification: math.FA
Remarks: 7 pages
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.4814
or
http://arXiv.org/abs/1107.4814
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yanqi Qiu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Aug 2011 15:33:53 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the operator space $OUMD$
property for the column Hilbert space $C$" by Yanqi Qiu.
Abstract: The operator space $OUMD$ property was introduced by Pisier in
the context of verctor-valued noncommutative $L_p$-spaces. It is still
unknown whether the property is independent of $p$ in this setting. In
this paper, we prove that the column Hilbert space $C$ is $OUMD_p$ for
all $1 < p < \infty$, this answers positively a question asked by Ruan.
Archive classification: math.FA math.OA
Submitted from: yqi.qiu at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1107.4941
or
http://arXiv.org/abs/1107.4941
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stephen Sanchez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Aug 2011 15:36:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the supremal $p$-negative type
of a finite metric space" by Stephen Sanchez.
Abstract: We study the supremal $p$-negative type of finite metric
spaces. An explicit expression for the supremal $p$-negative type $\wp
(X,d)$ of a finite metric space $(X,d)$ is given in terms its associated
distance matrix, from which the supremal $p$-negative type of the space
may be calculated. The method is then used to give a straightforward
calculation of the supremal $p$-negative type of the complete bipartite
graphs $K_{n,m}$ endowed with the usual path metric. A gap in the spectrum
of possible supremal $p$-negative type values of path metric graphs is
also proven.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 51F99 (Primary) 46B85, 54E35
(Secondary)
Remarks: 11 pages, 6 figures
Submitted from: stephen.sanchez at unsw.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.0451
or
http://arXiv.org/abs/1108.0451
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Diogo Diniz, G. A. Munoz-Fernandez, Daniel
Pellegrino and J. B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 26 Aug 2011 15:41:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The asymptotic growth of
the constants in the Bohnenblust-Hille inequality is optimal"
by Diogo Diniz, G. A. Munoz-Fernandez, Daniel Pellegrino and
J. B. Seoane-Sepulveda.
Abstract: In this note we provide a family of constants,
$C_{n}$, enjoying the Bohnenblust--Hille inequality and such that
$\lim_{n\rightarrow\infty}C_{n}/C_{n-1}=1$, i.e., their asymptotic growth
is the best possible. As a consequence, we also show that the optimal
constants, $K_n$, in the Bohnenblust--Hille inequality have the best
possible asymptotic behavior.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.1550
or
http://arXiv.org/abs/1108.1550
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Grigory L. Litvinov
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 15:43:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximation properties of
locally convex spaces and the problem of uniqueness of the trace of a
linear operator" by Grigory L. Litvinov.
Abstract: In the present article, it is proved that every nuclear
operator in a locally convex space E has a well-defined trace if
E possesses the approximation property. However, even if a space
possesses the approximation property this still does not guarantee
a positive solution of A. Grothendieck's uniqueness problem for this
space. Below, we present an example of a quasi-complete space with the
approximation property in which it is not possible to define the trace
for all Fredholm operators (in the sense of A. Grothendieck). We prove
that the uniqueness problem has a positive solution if E possesses the
"bounded approximation property." Preliminary information and results
are presented in Section 2. A number of approximation-type properties
of locally convex spaces and relations between these properties are
considered in Section 3. The principal results of the present study,
along with certain corollaries from these results (for example, the
existence of a matrix trace), may be found in Section 4.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46A32, 46A35
Citation: Selecta Mathematica Sovietica, vol. 11, No.1 (1992), p. 25-40
Remarks: 18 pages
Submitted from: glitvinov at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.1721
or
http://arXiv.org/abs/1108.1721
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Subhash Khot and Assaf Naor
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 15:45:27 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Grothendieck-type inequalities
in combinatorial optimization" by Subhash Khot and Assaf Naor.
Abstract: We survey connections of the Grothendieck inequality and its
variants to combinatorial optimization and computational complexity.
Archive classification: cs.DS cs.CC math.CO math.FA
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.2464
or
http://arXiv.org/abs/1108.2464
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 15:53:57 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Low-distortion embeddings of
graphs with large girth" by Mikhail I. Ostrovskii.
Abstract: The main purpose of the paper is to construct a sequence of
graphs of constant degree with indefinitely growing girths admitting
embeddings into $\ell_1$ with uniformly bounded distortions. This result
answers the problem posed by N.~Linial, A.~Magen, and A.~Naor (2002).
Archive classification: math.MG math.CO math.FA
Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12,
54E35
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.2542
or
http://arXiv.org/abs/1108.2542
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Turdebek N. Bekjan and Zeqian Chen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 15:59:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Noncommutative integral
inequalities for convex functions of maximal functions and applications"
by Turdebek N. Bekjan and Zeqian Chen.
Abstract: In this paper, we establish a Marcinkiewicz type interpolation
theorem for convex functions of maximal functions in the noncommutative
setting. As applications, we prove the noncommutative analogue of the
Doob inequality for convex functions of maximal functions on martingales,
the analogue of the classical Dunford-Schwartz maximal ergodic inequality
for convex functions of positive contractions, and that of Stein's maximal
inequality for convex functions of symmetric positive contractions. As
a consequence, we obtain the moment Burkholder-Davis-Gundy inequality
for noncommutative martingales.
Archive classification: math.FA math.PR
Remarks: 18 pages
Submitted from: chenzeqian at hotmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.2795
or
http://arXiv.org/abs/1108.2795
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Veronica Dimant, Daniel Galicer and Ricardo
Garcia
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 16:01:45 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Geometry of integral polynomials,
$M$-ideals and unique norm preserving extensions" by Veronica Dimant,
Daniel Galicer and Ricardo Garcia.
Abstract: We use the Aron-Berner extension to prove that the set of
extreme points of the unit ball of the space of integral polynomials
over a real Banach space $X$ is $\{\pm \phi^k: \phi \in X^*, \|
\phi\|=1\}$. With this description we show that, for real Banach
spaces $X$ and $Y$, if $X$ is a non trivial $M$-ideal in $Y$, then
$\widehat\bigotimes^{k,s}_{\varepsilon_{k,s}} X$ (the $k$-th symmetric
tensor product of $X$ endowed with the injective symmetric tensor norm) is
\emph{never} an $M$-ideal in $\widehat\bigotimes^{k,s}_{\varepsilon_{k,s}}
Y$. This result marks up a difference with the behavior of non-symmetric
tensors since, when $X$ is an $M$-ideal in $Y$, it is known that
$\widehat\bigotimes^k_{\varepsilon_k} X$ (the $k$-th tensor product
of $X$ endowed with the injective tensor norm) is an $M$-ideal in
$\widehat\bigotimes^k_{\varepsilon_k} Y$. Nevertheless, if $X$ is Asplund,
we prove that every integral $k$-homogeneous polynomial in $X$ has a
unique extension to $Y$ that preserves the integral norm. We explicitly
describe this extension.
We also give necessary and sufficient conditions (related with the
continuity of the Aron-Berner extension morphism) for a fixed
$k$-homogeneous polynomial $P$ belonging to a maximal polynomial ideal
$\Q(^kX)$ to have a unique norm preserving extension to $\Q(^kX^{**})$. To
this end, we study the relationship between the bidual of the symmetric
tensor product of a Banach space and the symmetric tensor product of its
bidual and show (in the presence of the BAP) that both spaces have `the
same local structure'. Other applications to the metric and isomorphic
theory of symmetric tensor products and polynomial ideals are also given.
Archive classification: math.FA
Mathematics Subject Classification: 46G25, 46M05, 46B28
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/1108.3975
or
http://arXiv.org/abs/1108.3975
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Emanuel Milman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 16:07:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Sharp isoperimetric inequalities and
model spaces for curvature-dimension-diameter condition" by Emanuel Milman.
Abstract: We obtain new sharp isoperimetric inequalities on a Riemannian
manifold equipped with a probability measure, whose generalized Ricci
curvature is bounded from below (possibly negatively), and generalized
dimension and diameter of the convex support are bounded from above
(possibly infinitely). Our inequalities are \emph{sharp} for sets
of any given measure and with respect to all parameters (curvature,
dimension and diameter). Moreover, for each choice of parameters, we
identify the \emph{model spaces} which are extremal for the isoperimetric
problem. In particular, we recover the Gromov--L\'evy and Bakry--Ledoux
isoperimetric inequalities, which state that whenever the curvature is
strictly \emph{positively} bounded from below, these model spaces are
the $n$-sphere and Gauss space, corresponding to generalized dimension
being $n$ and $\infty$, respectively. In all other cases, which seem new
even for the classical Riemannian-volume measure, it turns out that there
is no \emph{single} model space to compare to, and that a simultaneous
comparison to a natural \emph{one parameter family} of model spaces is
required, nevertheless yielding a sharp result.
Archive classification: math.DG math.FA math.MG
Mathematics Subject Classification: 32F32, 53C21, 53C20
Remarks: 36 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/1108.4609
or
http://arXiv.org/abs/1108.4609
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Boaz Klartag and Emanuel Milman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 16:18:06 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Inner regularization of log-concave
measures and small-ball estimates" by Boaz Klartag and Emanuel Milman.
Authors: Bo'az Klartag and Emanuel Milman
Abstract: In the study of concentration properties of isotropic
log-concave measures, it is often useful to first ensure that the measure
has super-Gaussian marginals. To this end, a standard preprocessing step
is to convolve with a Gaussian measure, but this has the disadvantage of
destroying small-ball information. We propose an alternative preprocessing
step for making the measure seem super-Gaussian, at least up to reasonably
high moments, which does not suffer from this caveat: namely, convolving
the measure with a random orthogonal image of itself. As an application
of this ``inner-thickening", we recover Paouris' small-ball estimates.
Archive classification: math.FA
Remarks: 12 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/1108.4856
or
http://arXiv.org/abs/1108.4856
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Horst Martini, Konrad J. Swanepoel, and P.
Oloff de Wet
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 16:23:26 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Absorbing angles, Steiner minimal
trees, and antipodality" by Horst Martini, Konrad J. Swanepoel, and
P. Oloff de Wet.
Abstract: We give a new proof that a star $\{op_i:i=1,\dots,k\}$
in a normed plane is a Steiner minimal tree of its vertices
$\{o,p_1,\dots,p_k\}$ if and only if all angles formed by the edges at
$o$ are absorbing [Swanepoel, Networks \textbf{36} (2000), 104--113]. The
proof is more conceptual and simpler than the original one.
We also find a new sufficient condition for higher-dimensional normed
spaces to share this characterization. In particular, a star $\{op_i:
i=1,\dots,k\}$ in any CL-space is a Steiner minimal tree of its vertices
$\{o,p_1,\dots,p_k\}$ if and only if all angles are absorbing, which
in turn holds if and only if all distances between the normalizations
$\frac{1}{\|p_i\|}p_i$ equal $2$. CL-spaces include the mixed $\ell_1$
and $\ell_\infty$ sum of finitely many copies of $R^1$.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B20 (Primary). 05C05, 49Q10, 52A21
(Secondary)
Citation: Journal of Optimization Theory and Applications, 143 (2009),
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.5046
or
http://arXiv.org/abs/1108.5046
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Almut Burchard
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 16:25:58 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Rate of convergence of random
polarizations" by Almut Burchard.
Abstract: After n random polarizations of Borel set on a sphere, its
expected symmetric difference from a polar cap is bounded by C/n, where
the constant depends on the dimension [arXiv:1104.4103]. We show here
that this power law is best possible, and that the constant grows at
least linearly with the dimension.
Archive classification: math.PR math.FA
Remarks: 5 pages
Submitted from: almut at math.toronto.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.5500
or
http://arXiv.org/abs/1108.5500
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Kaminska, Alexey I. Popov, Eugeniu
Spinu, Adi Tcaciuc, and Vladimir G. Troitsky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 9 Sep 2011 16:27:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Norm closed operator ideals in
Lorentz sequence spaces" by Anna Kaminska, Alexey I. Popov, Eugeniu Spinu,
Adi Tcaciuc, and Vladimir G. Troitsky.
Abstract: In this paper, we study the structure of closed algebraic
ideals in the algebra of operators acting on a Lorentz sequence space.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 47L20. Secondary: 47B10,
47B37
Remarks: 25 pages
Submitted from: troitsky at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1108.6026
or
http://arXiv.org/abs/1108.6026
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 29 Sep 2011 15:10:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Real interpolation and
transposition of certain function spaces" by Gilles Pisier.
Abstract: Our starting point is a lemma due to Varopoulos. We give
a different proof of a generalized form this lemma, that yields an
equivalent description of the $K$-functional for the interpolation
couple $(X_0,X_1)$ where $X_0=L_{p_0,\infty}(\mu_1; L_q(\mu_2))$ and
$X_1=L_{p_1,\infty}(\mu_2; L_q(\mu_1))$ where $0<q<p_0,p_1\le \infty$ and
$(\Omega_1,\mu_1), (\Omega_2,\mu_2)$ are arbitrary measure spaces. When
$q=1$, this implies that the space $(X_0,X_1)_{\theta,\infty}$
($0<\theta<1$) can be identified with a certain space of operators. We
also give an extension of the Varopoulos Lemma to pairs (or finite
families) of conditional expectations that seems of independent
interest. The present paper is motivated by non-commutative applications
that we choose to publish separately.
Archive classification: math.FA
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.1006
or
http://arXiv.org/abs/1109.1006
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Alistair Bird, Graham Jameson and Niels
Jakob Laustsen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 29 Sep 2011 15:12:35 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Giesy--James theorem for
general index $p$, with an application to operator ideals on the $p$th
James space" by Alistair Bird, Graham Jameson and Niels Jakob Laustsen.
Abstract: A theorem of Giesy and James states that $c_0$ is finitely
representable in James' quasi-reflexive Banach space $J_2$. We extend this
theorem to the $p$th quasi-reflexive James space $J_p$ for each $p \in
(1,\infty)$. As an application, we obtain a new closed ideal of operators
on $J_p$, namely the closure of the set of operators that factor through
the complemented subspace $(\ell_\infty^1 \oplus \ell_\infty^2 \oplus
\cdots \oplus \ell_\infty^n \oplus \cdots)_{\ell_p}$ of $J_p$.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46B45, 47L20 (Primary) 46B07, 46H10,
47L10 (Secondary)
Remarks: 16 pages
Submitted from: alistairbird at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.1776
or
http://arXiv.org/abs/1109.1776
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gilles Pisier
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 29 Sep 2011 15:14:03 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Real interpolation between row
and column spaces" by Gilles Pisier.
Abstract: We give an equivalent expression for the $K$-functional
associated to the pair of operator spaces $(R,C)$ formed by the rows
and columns respectively. This yields a description of the real
interpolation spaces for the pair $(M_n(R), M_n(C))$ (uniformly over
$n$). More generally, the same result is valid when $M_n$ (or $B(\ell_2)$)
is replaced by any semi-finite von~Neumann algebra. We prove a version
of the non-commutative Khintchine inequalities (originally due to
Lust--Piquard) that is valid for the Lorentz spaces $L_{p,q}(\tau)$
associated to a non-commutative measure $\tau$, simultaneously for the
whole range $1\le p,q< \infty$, regardless whether $p<2 $ or $p>2$.
Actually, the main novelty is the case $p=2,q\not=2$. We also prove a
certain simultaneous decomposition property for the operator norm and
the Hilbert-Schmidt one.
Archive classification: math.OA
Mathematics Subject Classification: 47B10
Submitted from: pisier at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.1860
or
http://arXiv.org/abs/1109.1860
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Dario Cordero-Erausquin and Boaz Klartag
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 29 Sep 2011 15:16:07 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Interpolations, convexity and
geometric inequalities" by Dario Cordero-Erausquin and Boaz Klartag.
Abstract: We survey some interplays between spectral estimates of
H\"ormander-type, degenerate Monge-Amp\`ere equations and geometric
inequalities related to log-concavity such as Brunn-Minkowski, Santal\'o
or Busemann inequalities.
Archive classification: math.FA math.CV
Submitted from: cordero at math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.3652
or
http://arXiv.org/abs/1109.3652
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: Thu, 29 Sep 2011 15:17:43 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the existence of universal
series by trigonometric system" by Sergo A. Episkoposian.
Abstract: In this paper we prove the following: let $\omega(t)$ be a
continuous function, increasing in $[0,\infty)$ and $\omega(+0)=0$. Then
there exists a series of the form
$$\sum_{k=-\infty}^\infty C_ke^{ikx} \ \ with \ \
\sum_{k=-\infty}^\infty
C^2_k \omega(|C_k|)<\infty ,\ \ C_{-k}=\overline{C}_k, \eqno$$ with
the following property: for each $\varepsilon>0$ a weighted function
$\mu(x), 0<\mu(x) \le1, \left | \{ x\in[0,2\pi]: \mu(x)\not =1 \} \right
| <\varepsilon $ can be constructed, so that the series is universal in
the weighted space $L_\mu^1[0,2\pi]$ with respect to rearrangements.
Archive classification: math.FA
Mathematics Subject Classification: 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/1109.3805
or
http://arXiv.org/abs/1109.3805
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: Thu, 29 Sep 2011 15:19:19 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On greedy algorithms with respect
to generalized Walsh system" by Sergo A. Episkoposian.
Abstract: In this paper we proof that there exists a function f(x)
belongs to L^1[0,1] such that a greedy algorithm
with regard to generalized Walsh system does not converge to f(x)
in L^1[0,1] norm, i.e. the generalized Walsh system is not a
quasi-greedy basis in its linear span L^1[0,1].
Archive classification: math.FA
Mathematics Subject Classification: 42C10, 46E30
Submitted from: sergoep at ysu.am
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.3806
or
http://arXiv.org/abs/1109.3806
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Parcet Javier, Soria Fernando, and Xu
Quanhua
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 29 Sep 2011 15:20:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the growth of vector-valued
Fourier series" by Parcet Javier, Soria Fernando, and Xu Quanhua.
Abstract: We prove the 'little Carleson theorem' on the growth of Fourier
series for functions taking values in a UMD Banach space.
Archive classification: math.CA math.FA
Submitted from: javier.parcet at icmat.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.4313
or
http://arXiv.org/abs/1109.4313
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Adriano Thiago Bernardino, Daniel
Pellegrino and Juan B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 29 Sep 2011 15:22:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Multiple $(p;q;r)$-summing
polynomials and multilinear operators" by Adriano Thiago Bernardino,
Daniel Pellegrino and Juan B. Seoane-Sepulveda.
Abstract: The concept of absolutely $(p;q;r)$-summing linear operators is
due to A. Pietsch; it is a natural extension of the classical notion of
absolutely $(p;q)$-summing operators. Very recently D. Achour introduced
the concept of absolutely $(p;q;r)$-summing multilinear mappings. In this
paper we obtain some properties of this class and show that the polynomial
version of this notion is neither coherent nor compatible (according to
the definition of Carando, Dimant, and Muro). Here we shall provide an
alternative approach that generates coherent and compatible ideals.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.4898
or
http://arXiv.org/abs/1109.4898
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Konrad J. Swanepoel and Rafael Villa
From: alspach at math.okstate.edu (Dale Alspach)
Date: Thu, 29 Sep 2011 15:23:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Maximal equilateral sets" by
Konrad J. Swanepoel and Rafael Villa.
Abstract: A subset of a normed space X is called equilateral if the
distance between any two points is the same. Let m(X) be the smallest
possible size of an equilateral subset of X maximal with respect to
inclusion. We first observe that Petty's construction of a d-dimensional
X of any finite dimension d >= 4 with m(X)=4 can be generalised to show
that m(X\oplus_1\R)=4 for any X of dimension at least 2 which has a
smooth point on its unit sphere. By a construction involving Hadamard
matrices we then show that both m(\ell_p) and m(\ell_p^d) are finite and
bounded above by a function of p, for all 1 <= p < 2. Also, for all p in
[1,\infty) and natural numbers d there exists c=c(p,d) > 1 such that m(X)
<= d+1 for all d-dimensional X with Banach-Mazur distance less than c
from \ell_p^d. Using Brouwer's fixed-point theorem we show that m(X)
<= d+1 for all d-\dimensional X with Banach-Mazur distance less than
3/2 from \ell_\infty^d. A graph-theoretical argument furthermore shows
that m(\ell_\infty^d)=d+1.
The above results lead us to conjecture that m(X) <= 1+\dim X.
Archive classification: math.MG math.CO math.FA
Mathematics Subject Classification: 46B20 (Primary), 46B85, 52A21, 52C17
(Secondary)
Remarks: 15 pages
Submitted from: konrad.swanepoel at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5063
or
http://arXiv.org/abs/1109.5063
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Sergey Bobkov and Mokshay Madiman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:29:54 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Reverse Brunn-Minkowski and reverse
entropy power inequalities for convex measures" by Sergey Bobkov and
Mokshay Madiman.
Abstract: We develop a reverse entropy power inequality for convex
measures, which may be seen as an affine-geometric inverse of the
entropy power inequality of Shannon and Stam. The specialization of this
inequality to log-concave measures may be seen as a version of Milman's
reverse Brunn-Minkowski inequality. The proof relies on a demonstration
of new relationships between the entropy of high dimensional random
vectors and the volume of convex bodies, and on a study of effective
supports of convex measures, both of which are of independent interest,
as well as on Milman's deep technology of $M$-ellipsoids and on certain
information-theoretic inequalities. As a by-product, we also give a
continuous analogue of some Pl\"unnecke-Ruzsa inequalities from additive
combinatorics.
Archive classification: math.FA math.PR
Remarks: 28 pages, revised version of a document submitted in October 2010
Submitted from: mokshay.madiman at yale.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5287
or
http://arXiv.org/abs/1109.5287
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Casey Kelleher, Daniel Miller, Trenton
Osborn, and Anthony Weston
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:31:12 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strongly non embeddable metric
spaces" by Casey Kelleher, Daniel Miller, Trenton Osborn, and Anthony
Weston.
Abstract: Enflo constructed a countable metric space that may not
be uniformly embedded into any metric space of positive generalized
roundness. Dranishnikov, Gong, Lafforgue and Yu modified Enflo's
example to construct a locally finite metric space that may not be
coarsely embedded into any Hilbert space. In this paper we meld these two
examples into one simpler construction. The outcome is a locally finite
metric space $(\mathfrak{Z}, \zeta)$ which is strongly non embeddable
in the sense that it may not be embedded uniformly or coarsely into
any metric space of non zero generalized roundness. Moreover, we show
that both types of embedding may be obstructed by a common recursive
principle. It follows from our construction that any metric space which
is Lipschitz universal for all locally finite metric spaces may not
be embedded uniformly or coarsely into any metric space of non zero
generalized roundness. Our construction is then adapted to show that
the group $\mathbb{Z}_\omega=\bigoplus_{\aleph_0}\mathbb{Z}$ admits a
Cayley graph which may not be coarsely embedded into any metric space
of non zero generalized roundness. Finally, for each $p \geq 0$ and
each locally finite metric space $(Z,d)$, we prove the existence of a
Lipschitz injection $f : Z \to \ell_{p}$.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46C05, 46T99
Remarks: 10 pages
Submitted from: westona at canisius.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5300
or
http://arXiv.org/abs/1109.5300
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Qingying Bu, Gerard Buskes, Alexey I.
Popov, Adi Tcaciuc, and Vladimir G. Troitsky
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:33:02 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The 2-concavification of a Banach
lattice equals the diagonal of the Fremlin tensor square" by Qingying
Bu, Gerard Buskes, Alexey I. Popov, Adi Tcaciuc, and Vladimir G. Troitsky.
Abstract: We investigate the relationship between the diagonal of the
Fremlin projective tensor product of a Banach lattice $E$ with itself
and the 2-concavification of~$E$.
Archive classification: math.FA
Mathematics Subject Classification: 46B42, 46M05, 46B40, 46B45
Remarks: 18 pages
Submitted from: troitsky at ualberta.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5380
or
http://arXiv.org/abs/1109.5380
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Kaminska and Damian Kubiak
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:34:41 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the dual of Ces\`aro function
space" by Anna Kaminska and Damian Kubiak.
Abstract: The goal of this paper is to present an isometric representation
of the dual space to Ces\`aro function space $C_{p,w}$, $1<p<\infty$,
induced by arbitrary positive weight function $w$ on interval $(0,l)$
where $0<l\leqslant\infty$. For this purpose given a strictly
decreasing nonnegative function $\Psi$ on $(0,l)$, the notion of
essential $\Psi$-concave majorant $\hat f$ of a measurable function $f$
is introduced and investigated. As applications it is shown that every
slice of the unit ball of the Ces\`aro function space has diameter
2. Consequently Ces\`aro function spaces do not have the Radon-Nikodym
property, are not locally uniformly convex and they are not dual spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46E30, 46B20, 46B42, 46B22
Remarks: 15 pages
Submitted from: dmkubiak at memphis.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5400
or
http://arXiv.org/abs/1109.5400
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ondrej Kurka
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:36:09 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Genericity of Fr\'echet smooth
spaces" by Ondrej Kurka.
Abstract: If a separable Banach space contains an isometric copy of
every separable reflexive Fr\'echet smooth Banach space, then it contains
an isometric copy of every separable Banach space. The same conclusion
holds if we consider separable Banach spaces with Fr\'echet smooth dual
space. This improves a result of G. Godefroy and N. J. Kalton.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04, 46B20, Secondary
46B15, 54H05
Remarks: 34 pages
Submitted from: kurka.ondrej at seznam.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5726
or
http://arXiv.org/abs/1109.5726
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Anna Pelczar-Barwacz
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:37:30 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strictly singular operators in
asymptotic $\ell_p$ Banach spaces" by Anna Pelczar-Barwacz.
Abstract: We present condition on higher order asymptotic behaviour of
basic sequences in a Banach space ensuring the existence of bounded
non-compact strictly singular operator on a subspace. We apply it in
asymptotic $\ell_p$ spaces, $1\leq p<\infty$, in particular in convexified
mixed Tsirelson spaces and related asymptotic $\ell_p$ HI spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B06
Remarks: 19 pages
Submitted from: anna.pelczar at im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.5874
or
http://arXiv.org/abs/1109.5874
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jipu Ma
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:39:56 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A geometry characteristic for
Banach space with $c^1$-norm" by Jipu Ma.
Abstract: Let $E$ be a Banach space with the $c^1$-norm $\|\cdot\|$
in $ E \backslash \{0\}$ and $S(E)=\{e\in E: \|e\|=1\}.$ In this paper,
a geometry characteristic for $E$ is presented by using a geometrical
construct of $S(E).$ That is, the following theorem holds : the norm
of $E$ is of $c^1$ in $ E \backslash \{0\}$ if and only if $S(E)$ is a
$c^1$-submanifold of $E,$ with ${\rm codim}S(E)=1.$ The theorem is very
clear, however, its proof is non-trivial, which shows an intrinsic
connection between the continuous differentiability of the norm
$\|\cdot\|$ in $ E \backslash \{0\}$ and differential structure of $S(E).$
Archive classification: math.FA
Mathematics Subject Classification: 54Exx, 46Txx, 58B20
Submitted from: huangql at yzu.edu.cn
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.6823
or
http://arXiv.org/abs/1109.6823
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Geraldo Botelho, Daniel Cariello, Vinicius
Favaro and Daniel Pellegrino
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:41:24 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Maximal spaceability in topological
vector spaces" by Geraldo Botelho, Daniel Cariello, Vinicius Favaro and
Daniel Pellegrino.
Abstract: In this paper we introduce a new technique to prove the
existence of closed subspaces of maximal dimension inside sets of
topological vector sequence spaces. The results we prove cover some
sequence spaces not studied before in the context of spaceability and
settle some questions on classical sequence spaces that remained open.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1109.6863
or
http://arXiv.org/abs/1109.6863
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Wieslaw Kubis and Slawomir Solecki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:42:49 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A proof of uniqueness of the
Gurarii space" by Wieslaw Kubis and Slawomir Solecki.
Abstract: We present a short and elementary proof of isometric uniqueness
of the Gurarii space.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20
Remarks: 6 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/1110.0903
or
http://arXiv.org/abs/1110.0903
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Miroslav Kacena, Ondrej F.K. Kalenda and
Jiri Spurny
From: alspach at math.okstate.edu (Dale Alspach)
Date: Fri, 7 Oct 2011 14:44:48 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Quantitative Dunford-Pettis
property" by Miroslav Kacena, Ondrej F.K. Kalenda and Jiri Spurny.
Abstract: We investigate possible quantifications of the Dunford-Pettis
property. We show, in particular, that the Dunford-Pettis property is
automatically quantitative in a sense. Further, there are two incomparable
mutually dual stronger versions of a quantitative Dunford-Pettis
property. We investigate their relationship with a quantitative Schur
property and prove that $L^1$ spaces and $C(K)$ spaces posses both of
them. We also show that several natural measures of weak non-compactness
are equal in $L^1$ spaces.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B20, 47B07, 47B10
Remarks: 47 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/1110.1243
or
http://arXiv.org/abs/1110.1243
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: Tue, 1 Nov 2011 14:29:55 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Displaying Polish groups on
separable Banach spaces" by Valentin Ferenczi and Christian Rosendal.
Abstract: A display of a topological group G on a Banach space X is
a topological isomorphism of G with the isometry group Isom(X,||.||)
for some equivalent norm ||.|| on X, where the latter group is equipped
with the strong operator topology.
Displays of Polish groups on separable real spaces are studied. It
is proved that any closed subgroup of the infinite symmetric group
S_\infty containing a non-trivial central involution admits a display
on any of the classical spaces c0, C([0,1]), lp and Lp for 1 <=p
<\infty. Also, for any Polsih group G, there exists a separable space
X on which {-1,1} x G has a display.
Archive classification: math.GR math.FA math.LO
Mathematics Subject Classification: 20E08, 03E15, 46B03
Remarks: 27 pages
Submitted from: ferenczi at ccr.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1110.2970
or
http://arXiv.org/abs/1110.2970
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Daniel Galicer, Silvia Lassalle and Pablo
Turco
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:31:20 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The ideal of p-compact operators:
a tensor product approach" by Daniel Galicer, Silvia Lassalle and
Pablo Turco.
Abstract: We study the space of $p$-compact operators $\mathcal K_p$,
using the theory of tensor norms and operator ideals. We prove that
$\mathcal K_p$ is associated to $/d_p$, the left injective associate of
the Chevet-Saphar tensor norm $d_p$ (which is equal to $g_{p'}'$). This
allows us to relate the theory of $p$-summing operators with that of
$p$-compact operators. With the results known for the former class and
appropriate hypothesis on $E$ and $F$ we prove that $\mathcal K_p(E;F)$
is equal to $\mathcal K_q(E;F)$ for a wide range of values of $p$ and $q$,
and show that our results are sharp. We also exhibit several structural
properties of $\mathcal K_p$. For instance, we obtain that $\mathcal
K_p$ is regular, surjective, totally accessible and characterize its
maximal hull $\mathcal K_p^{max}$ as the dual ideal of the $p$-summing
operators, $\Pi_p^{dual}$. Furthermore, we prove that $\mathcal K_p$
coincides isometrically with $\mathcal {QN}_p^{dual}$, the dual ideal
of the quasi $p$-nuclear operators.
Archive classification: math.FA
Mathematics Subject Classification: 47L20, 46A32, 47B07, 47B10
Remarks: 18 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/1110.3251
or
http://arXiv.org/abs/1110.3251
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Jakub Olejnik
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:32:46 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On a complete characterization
of a.s.\ convergence of multiple orthogonal series" by Jakub Olejnik.
Abstract: We present a relation between convergence of multiple and single
orthogonal series. This relation implies a complete characterization of
all multiple sequences $(a_{n_1\ldots n_d})_{n_1,\ldots,n_d\in\bb N}$
such that for all orthonormal $(\Phi_{n_1\ldots n_d})$ multiple orthogonal
series $\sum_{n_1,\ldots,n_d\in\bb N}a_{n_1\ldots n_d}\Phi_{n_1\ldots
n_d}$ are a.s.\ convergent.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 60G60, 60G17 (MSC2010)
Submitted from: jakubo at math.uni.lodz.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1110.3942
or
http://arXiv.org/abs/1110.3942
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ohad Giladi, Assaf Naor, and Gideon
Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:34:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Bourgain's discretization theorem"
by Ohad Giladi, Assaf Naor, and Gideon Schechtman.
Abstract: Bourgain's discretization theorem asserts that there exists
a universal constant $C\in (0,\infty)$ with the following property. Let
$X,Y$ be Banach spaces with $\dim X=n$. Fix $D\in (1,\infty)$ and set $\d=
e^{-n^{Cn}}$. Assume that $\mathcal N$ is a $\d$-net in the unit ball of
$X$ and that $\mathcal N$ admits a bi-Lipschitz embedding into $Y$ with
distortion at most $D$. Then the entire space $X$ admits a bi-Lipschitz
embedding into $Y$ with distortion at most $CD$. This mostly expository
article is devoted to a detailed presentation of a proof of Bourgain's
theorem.
We also obtain an improvement of Bourgain's theorem in the important
case when $Y=L_p$ for some $p\in [1,\infty)$: in this case it suffices to
take $\delta= C^{-1}n^{-5/2}$ for the same conclusion to hold true. The
case $p=1$ of this improved discretization result has the following
consequence. For arbitrarily large $n\in \N$ there exists a family
$\mathscr Y$ of $n$-point subsets of $\{1,\ldots,n\}^2\subseteq \R^2$ such
that if we write $|\mathscr Y|= N$ then any $L_1$ embedding of $\mathscr
Y$, equipped with the Earthmover metric (a.k.a. transportation cost metric
or minimumum weight matching metric) incurs distortion at least a constant
multiple of $\sqrt{\log\log N}$; the previously best known lower bound
for this problem was a constant multiple of $\sqrt{\log\log \log N}$.
Archive classification: math.FA math.MG
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1110.5368
or
http://arXiv.org/abs/1110.5368
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S.Waleed Noor and Dan Timotin
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:35:50 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Embeddings of M\"{u}ntz spaces:
the Hilbertian case" by S.Waleed Noor and Dan Timotin.
Abstract: Given a strictly increasing sequence $\Lambda=(\lambda_n)$
of nonegative real numbers, with $\sum_{n=1}^\infty
\frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined
as the closure in $L^p([0,1])$ of the monomials $x^{\lambda_n}$. We
discuss properties of the embedding $M_\Lambda^p\subset L^p(\mu)$, where
$\mu$ is a finite positive Borel measure on the interval $[0,1]$. Most
of the results are obtained for the Hilbertian case $p=2$, in which we
give conditions for the embedding to be bounded, compact, or to belong
to the Schatten--von Neumann ideals.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 46E15, 46E20, 46E35
Submitted from: dtimotin at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1110.5422
or
http://arXiv.org/abs/1110.5422
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. Artstein-Avidan, B. Klartag, C. Schuett
and E. Werner
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:37:14 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Functional affine-isoperimetry
and an inverse logarithmic Sobolev inequality" by S. Artstein-Avidan,
B. Klartag, C. Schuett and E. Werner.
Abstract: We give a functional version of the affine isoperimetric
inequality for log-concave functions which may be interpreted as
an inverse form of a logarithmic Sobolev inequality inequality for
entropy. A linearization of this inequality gives an inverse inequality
to the Poincar'e inequality for the Gaussian measure.
Archive classification: math.FA
Mathematics Subject Classification: 52A20
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/1110.5551
or
http://arXiv.org/abs/1110.5551
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Heinz H. Bauschke, Jonathan M. Borwein,
Xianfu Wang, and Liangjin Yao
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:38:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Br\'ezis-Browder Theorem
in a general Banach space" by Heinz H. Bauschke, Jonathan M. Borwein,
Xianfu Wang, and Liangjin Yao.
Abstract: During the 1970s Br\'ezis and Browder presented a now classical
characterization of maximal monotonicity of monotone linear relations
in reflexive spaces. In this paper, we extend and refine their result
to a general Banach space.
Archive classification: math.FA math.OC
Mathematics Subject Classification: Primary 47A06, 47H05, Secondary 47B65,
47N10, 90C25
Remarks: 23 pages
Submitted from: liangjinyao at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1110.5706
or
http://arXiv.org/abs/1110.5706
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Pedro L. Kaufmann and Leonardo Pellegrini
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:42:39 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Spaceability of sets of nowhere
$L^q$ functions" by Pedro L. Kaufmann and Leonardo Pellegrini.
Abstract: We say that a function $f:[0,1]\rightarrow \R$ is \emph{nowhere
$L^q$} if, for each nonvoid open subset $U$ of $[0,1]$, the restriction
$f|_U$ is not in $L^q(U)$. For a fixed $1\leq p <\infty$, we will show
that the set $$ S_p\doteq \{f\in L^p[0,1]: f\mbox{ is nowhere $L^q$, for
each }p<q\leq\infty\}, $$ united with $\{0\}$, contains an isometric and
complemented copy of $\ell_p$. In particular, this improves a result from
G. Botelho, V. F\'avaro, D. Pellegrino, and J. B. Seoane-Sep\'ulveda,
$L_p[0,1]\setminus \cup_{q>p} L_q[0,1]$ is spaceable for every $p>0$,
preprint, 2011., since $S_p$ turns out to be spaceable. In addition,
our result is a generalization of one of the main results from S. G\l
\c ab, P. L. Kaufmann, and L. Pellegrini, Spaceability and algebrability
of sets of nowhere integrable functions, preprint, 2011.
Archive classification: math.FA
Mathematics Subject Classification: 26A30
Submitted from: leoime at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/abs/1110.5774
or
http://arXiv.org/abs/abs/1110.5774
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tuomas P. Hytonen
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:44:46 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Foundations of vector-valued
singular integrals revisited---with random dyadic cubes" by Tuomas
P. Hytonen.
Abstract: The vector-valued $T(1)$ theorem due to Figiel, and a certain
square function estimate of Bourgain for translations of functions with
a limited frequency spectrum, are two cornerstones of harmonic analysis
in UMD spaces. In this paper, a simplified approach to these results
is presented, exploiting Nazarov, Treil and Volberg's method of random
dyadic cubes, which allows to circumvent the most subtle parts of the
original arguments.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 42B20, 60G46
Remarks: 12 pages
Submitted from: tuomas.hytonen at helsinki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1110.5826
or
http://arXiv.org/abs/1110.5826
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:46:16 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Euclidean sections of convex
bodies, series of lectures" by Gideon Schechtman.
Abstract: This is a somewhat expanded form of a four hours course given,
with small variations, first at the educational workshop Probabilistic
methods in Geometry, Bedlewo, Poland, July 6-12, 2008 and a few weeks
later at the Summer school on Fourier analytic and probabilistic methods
in geometric functional analysis and convexity, Kent, Ohio, August 13-20,
2008.\\ The main part of these notes gives yet another exposition of
Dvoretzky's theorem on Euclidean sections of convex bodies with a proof
based on Milman's. This material is by now quite standard. Towards the end
of these notes we discuss issues related to fine estimates in Dvoretzky's
theorem and there there are some results that didn't appear in print
before. In particular there is an exposition of an unpublished result
of Figiel (Claim \ref{claim:figiel}) which gives an upper bound on the
possible dependence on $\e$ in Milman's theorem. We would like to thank
Tadek Figiel for allowing us to include it here. There is also a better
version of the proof of one of the results from \cite{sc2} giving a lower
bound on the dependence on $\e$ in Dvoretzky's theorem. The improvement
is in the statement and proof of Proposition \ref{prop:main} here which
is a stronger version of the corresponding Corollary 1 in \cite{sc2}.
Archive classification: math.FA math.MG
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/1110.6401
or
http://arXiv.org/abs/1110.6401
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Gideon Schechtman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 1 Nov 2011 14:48:33 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Dimension reduction in $L_p$,
$0<p<2$" by Gideon Schechtman.
Abstract: Complementing a recent observation of Newman and Rabinovich
for $p=1$ we observe here that for all $0<p<2$ any $k$ points in $L_p$
embeds with distortion $(1+\e)$ into $\ell_p^n$ where $n$ is linear in $k$
(and polynomial in $\e^{-1}$).
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B85
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/1110.2148
or
http://arXiv.org/abs/1110.2148
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: Tue, 1 Nov 2011 14:50:36 -0500 (CDT)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Duality and distance formulas in
spaces defined by means of oscillation" by Karl-Mikael Perfekt.
Abstract: For the classical space of functions with bounded mean
oscillation, it is well known that VMO** = BMO and there are many
characterizations of the distance from a function f in BMO to VMO. When
considering the Bloch space, results in the same vein are available with
respect to the little Bloch space. In this paper such duality results and
distance formulas are obtained by pure functional analysis. Applications
include general M\"obius invariant spaces such as Q_K-spaces,
Lipschitz-H\"older spaces and rectangular BMO of several variables.
Archive classification: math.FA math.CV
Submitted from: perfekt at maths.lth.se
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1110.6766
or
http://arXiv.org/abs/1110.6766
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Meeting February 2012
From: "Gonzalez Ortiz, Manuel" <manuel.gonzalez at unican.es>
Date: Wed, 9 Nov 2011 11:51:08 +0000
To: "banach at cauchy.math.okstate.edu" <banach at math.okstate.edu>
ANNOUNCEMENT OF MEETING
Convexity in Banach spaces -- An homage to Piero Papini
Castro Urdiales (Cantabria, Spain), 20-24 February 2012
Convexity is a central topic with many applications in functional analysis,
geometry, mathematical economy, control theory, etc.
This edition of the Castro Urdiales Banach Space Meeting will be focused on
the study of convexity; with special emphasis in its applications to Banach
space theory.
The Meeting is dedicated to celebrate Professor Piero Papini, whose work
has
always been close to the study of convexity in normed spaces, on the
occasion
of his retirement.
The following mathematicians have accepted so far to deliver a plenary
conference:
Carlos Benitez (Univ. Extremadura)
- Polarization constants in inner product spaces.
Felix Cabello Sanchez (Univ. Extremadura)
- Mathematical ping-pong.
Vladimir Fonf (Ben Gurion Univ.)
- Polyhedral spaces.
Peter Gruber (Univ. Wien)
- Great personalities of convex geometry from antiquity up to the
present.
- Normal bundles of convex bodies.
Jose P. Moreno (Univ. Madrid)
- Diametrically complete sets.
Justo Puerto (Univ. Sevilla)
- Location problems, solutions, algorithms and the like.
David Yost (Univ. Ballarat)
- Constants and parameters in Banach spaces.
Additionally, those wishing to highlight some aspect of the career
or research of Prof. Papini, or to present new results in convexity,
will have the opportunity to deliver a short talk during the meeting.
Please fill the corresponding request in the registration form.
The meeting will be held in Castro Urdiales, a town by the sea in
the north of Spain, about 20 Km from Bilbao, at the C.I.E.M.
(Centro Internacional de Encuentros Matematicos)
For registration and more information, please go to the web-site
of the conference
http://www.ciem.unican.es/encuentros/banach/2012/
Organizing Committee: Marco Baronti (Genova), Jesus M. F. Castillo
(Badajoz)
Manuel Gonz\'alez (Santander) and Clemente Zanco (Milano).
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Position at U Missouri
From: Dale Alspach <alspach at math.okstate.edu>
Date: Wed, 09 Nov 2011 15:01:37 -0600
To: banach at math.okstate.edu
The Department of Mathematics at the University of Missouri-Columbia
invites applications for
a tenure-track position at the rank of assistant professor in the field of
Analysis to begin August 2012.
Candidates must present evidence of excellence in teaching and research and
must have earned a Ph.D.
or equivalent in Mathematics by August 15, 2012. The successful candidate
will be expected to conduct
independent research, teach undergraduate and graduate courses, obtain
external funding, and supervise
graduate student research. Applicants should submit a cover letter,
curriculum vitae, and statements of
research and teaching interests. In addition, arrangements should be made
for four letters of recommendation
to be submitted to the department. One of these should specifically address
teaching. Applicants should submit
all materials, including letters of reference, through MathJobs.org.
Screening of applicants will begin January 30, 2012 and will continue until
the position is filled.
The University of Missouri is an EEO/AA/ADA institution. If you have a
disability and need accommodations in
the job application process, please contact the MU ADA coordinator
(hensonl at missouri.edu).
_______________________________________________
Banach mailing list
Banach at cauchy.math.okstate.edu
http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Eugenio Hernandez
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:40:00 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lebesgue-Type inequalities for
quasi-greedy bases" by Eugenio Hernandez.
Abstract: We show that for quasi-greedy bases in real Banach spaces the
error of the thresholding greedy algorithm of order N is bounded by the
best N-term error of approximation times a constant which depends on
the democracy functions and the quasi-greedy constant of the basis.
Archive classification: math.FA
Mathematics Subject Classification: 41A65, 41A46, 41A17
Remarks: 8 pages
Submitted from: eugenio.hernandez at uam.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.0460
or
http://arXiv.org/abs/1111.0460
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marius Junge and Qiang Zeng
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:41:39 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Noncommutative Bennett and
Rosenthal Inequalities" by Marius Junge and Qiang Zeng.
Abstract: In this paper we extend Bennett's and Bernstein's inequality to
the noncommutative setting. In addition we provide an improved version
of the noncommutative Rosenthal inequality, essentially due to Nagaev,
Pinelis, and Pinelis, Utev for commutative random variables. We also
present new best constants in Rosenthal's inequality. Applying these
results to random Fourier projections, we recover and elaborate on
fundamental results from compressed sensing, due to Candes, Romberg,
and Tao.
Archive classification: math.PR math.FA math.OA
Mathematics Subject Classification: 46L53, 46L50, 60E15, 60F10, 94A12
Remarks: 28 pages
Submitted from: zeng8 at illinois.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.1027
or
http://arXiv.org/abs/1111.1027
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Cedric Arhancet
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:43:09 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Unconditionality, Fourier
multipliers and Schur multipliers" by Cedric Arhancet.
Abstract: Let $G$ be an infinite locally compact abelian group. If $X$
is Banach space, we show that if every bounded Fourier multiplier
$T$ on $L^2(G)$ has the property that $T\ot Id_X$ is bounded on
$L^2(G,X)$ then the Banach space $X$ is isomorphic to a Hilbert
space. Moreover, if $1<p<\infty$, $p\not=2$, we prove that there
exists a bounded Fourier multiplier on $L^p(G)$ which is not completely
bounded. Finally, we examine unconditionality from the point of view
of Schur multipliers. Indeed, we give several sufficient conditions to
know if a Banach space or an operator space is isomorphic to a Hilbert
space or completely isomorphic to an operator Hilbert space.
Archive classification: math.FA math.OA
Remarks: 16 pages
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/1111.1664
or
http://arXiv.org/abs/1111.1664
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by S. K. Mercourakis and G. Vassiliadis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:44:35 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Equilateral sets in infinite
dimensional Banach spaces" by S. K. Mercourakis and G. Vassiliadis.
Abstract: We show that every Banach space $X$ containing an isomorphic
copy of $c_0$ has an infinite equilateral set and also that if $X$ has a
bounded biorthogonal system of size $\alpha$ then it can be renormed so
as to admit an equilateral set of equal size. If $K$ is any compact non
metrizable space, then under a certain combinatorial condition on $K$
the Banach space $C(K)$ has an uncountable equilateral set.
Archive classification: math.FA math.MG
Mathematics Subject Classification: Primary 46B20, Secondary 46B26, 46B04
Remarks: 15 pages, no figures
Submitted from: smercour at math.uoa.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.2273
or
http://arXiv.org/abs/1111.2273
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Tal Weissblat
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:45:58 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Santalo region of a log-concave
function" by Tal Weissblat.
Abstract: In this paper we define the Santalo region and the Floating
body of a log-concave function. We then study their properties. Our
main result is that any relation of Floating body and Santalo region of
a convex body is translated to a relation of Floating body and Santalo
region of an even log-concave function
Archive classification: math.FA
Submitted from: talvisbl at post.tau.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.2409
or
http://arXiv.org/abs/1111.2409
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Diogo Diniz, Gustavo Munoz-Fernandez,
Daniel Pellegrino and Juan B. Seoane-Sepulveda
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:48:14 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Lower bounds for the constants
in the Bohnenblust-Hille inequality: the case of real scalars"
by Diogo Diniz, Gustavo Munoz-Fernandez, Daniel Pellegrino and Juan
B. Seoane-Sepulveda.
Abstract: The Bohnenblust-Hille inequality was obtained
in 1931 and (in the case of real scalars) asserts that
for every positive integer $N$ and every $m$-linear mapping
$T:\ell_{\infty}^{N}\times\cdots\times\ell_{\infty}^{N}\rightarrow
\mathbb{R}$ one has \begin{equation*} \left(
\sum\limits_{i_{1},...,i_{m}=1}^{N}\left\vert
T(e_{i_{^{1}}},...,e_{i_{m}})\right\vert ^{\frac{2m}{m+1}}\right)
^{\frac{m+1}{2m}}\leq C_{m}\left\Vert T\right\Vert , \end{equation*}
for some positive constant $C_{m}$. Since then, several authors obtained
upper estimates for the values of $C_{m}$. However, the novelty presented
in this short note is that we provide lower (and non-trivial) bounds
for $C_{m}$.
Archive classification: math.FA
Submitted from: dmpellegrino at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.3253
or
http://arXiv.org/abs/1111.3253
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Pavlos Motakis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:50:01 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A reflexive HI space with the
hereditary Invariant Subspace Property" by Spiros A. Argyros and Pavlos
Motakis.
Abstract: A reflexive hereditarily indecomposable Banach space
$\mathfrak{X}_{_{^\text{ISP}}}$ is presented, such that for every $Y$
infinite dimensional closed subspace of $\mathfrak{X}_{_{^\text{ISP}}}$
and every bounded linear operator $T:Y\rightarrow Y$, the operator $T$
admits a non-trivial closed invariant subspace.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45, 47A15
Remarks: 39 pages, no figures
Submitted from: pmotakis at central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.3603
or
http://arXiv.org/abs/1111.3603
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Christian Le Merdy
From: alspach at math.okstate.edu (Dale Alspach)
Date: Mon, 28 Nov 2011 13:51:11 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A sharp equivalence between
$H^\infty$ functional calculus and square function estimates" by
Christian Le Merdy.
Abstract: Let T_t = e^{-tA} be a bounded analytic semigroup on Lp, with
1<p<\infty. It is known that if A and its adjoint A^* both satisfy
square function estimates \bignorm{\bigl(\int_{0}^{\infty}\vert
A^{1/2} T_t(x)\vert^2\, dt\,\bigr)^{1/2}_{Lp} \lesssim \norm{x} and
\bignorm{\bigl(\int_{0}^{\infty}\vert A^{*}^{1/2} T_t^*(y)\vert^2\,
dt\,\bigr)^{1/2}_{Lp'} \lesssim \norm{y} for x in Lp and y in Lp',
then A admits a bounded H^{\infty}(\Sigma_\theta) functional calculus
for any \theta>\frac{\pi}{2}. We show that this actually holds true for
some \theta<\frac{\pi}{2}.
Archive classification: math.FA
Mathematics Subject Classification: 47A60, 47D06
Submitted from: clemerdy at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.3719
or
http://arXiv.org/abs/1111.3719
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Spiros A. Argyros and Kevin Beanland
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:29:53 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On spaces admitting no $\ell_p$
or $c_0$ spreading model" by Spiros A. Argyros and Kevin Beanland.
Abstract: It is shown that for each separable Banach space $X$ not
admitting $\ell_1$ as a spreading model there is a space $Y$ having $X$
as a quotient and not admitting any $\ell_p$ for $1 \leq p < \infty$
or $c_0$ as a spreading model.
We also include the solution to a question of W.B. Johnson and
H.P. Rosenthal on the existence of a separable space not admitting as
a quotient any space with separable dual.
Archive classification: math.FA
Mathematics Subject Classification: 46B06
Remarks: 17 pages
Submitted from: kbeanland at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.4714
or
http://arXiv.org/abs/1111.4714
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by J. Lopez-Abad and S. Todorcevic
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:31:16 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Positional graphs and conditional
structure of weakly null sequences" by J. Lopez-Abad and S. Todorcevic.
Abstract: We prove that, unless assuming additional set theoretical
axioms, there are no reflexive space without unconditional sequences
of density the continuum. We give for every integer $n$ there are
normalized weakly-null sequences of length $\om_n$ without unconditional
subsequences. This together with a result of \cite{Do-Lo-To} shows that
$\om_\omega$ is the minimal cardinal $\kappa$ that could possibly have
the property that every weakly null $\kappa$-sequence has an infinite
unconditional basic subsequence . We also prove that for every cardinal
number $\ka$ which is smaller than the first $\om$-Erd\"os cardinal there
is a normalized weakly-null sequence without subsymmetric subsequences.
Finally, we prove that mixed Tsirelson spaces of uncountable densities
must always contain isomorphic copies of either $c_0$ or $\ell_p$,
with $p\ge 1$.
Archive classification: math.FA math.LO
Mathematics Subject Classification: Primary 46B03, 03E35, Secondary 03E02,
03E55, 46B26, 46A35
Submitted from: abad at icmat.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.5150
or
http://arXiv.org/abs/1111.5150
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Frank Morgan and Aldo Pratelli
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:32:42 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Existence of isoperimetric regions
in $\R^n$ with density" by Frank Morgan and Aldo Pratelli.
Abstract: We prove the existence of isoperimetric regions in $\R^n$ with
density under various hypotheses on the growth of the density. Along
the way we prove results on the boundedness of isoperimetric regions.
Archive classification: math.FA math.AP
Remarks: 31 pages, 4 figures
Submitted from: aldo.pratelli at unipv.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.5160
or
http://arXiv.org/abs/1111.5160
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Joanna Garbulinska and Wiesaw Kubis
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:34:40 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Remarks on Gurarii spaces" by
Joanna Garbulinska and Wiesaw Kubis.
Abstract: We present selected known results and some of their
improvements, involving Gurarii spaces. A Banach space is Gurarii
if it has certain natural extension property for almost isometric
embeddings of finite-dimensional spaces. Deleting the word ``almost",
we get the notion of a strong Gurarii space. There exists a unique
(up to isometry) separable Gurarii space, however strong Gurarii spaces
cannot be separable. The structure of the class of non-separable Gurarii
spaces seems to be not very well understood. We discuss some of their
properties and state some open questions. In particular, we characterize
non-separable Gurarii spaces in terms of skeletons of separable subspaces,
we construct a non-separable Gurarii space with a projectional resolution
of the identity and we show that no strong Gurarii space can be weakly
Lindel\"of determined.
Archive classification: math.FA
Mathematics Subject Classification: 46B04, 46B20
Remarks: 30 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/1111.5840
or
http://arXiv.org/abs/1111.5840
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Andrzej Wisnicki
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:37:01 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the fixed points of nonexpansive
mappings in direct sums of Banach spaces" by Andrzej Wisnicki.
Abstract: We show that if a Banach space X has the weak fixed point
property for nonexpansive mappings and Y has the generalized Gossez-Lami
Dozo property or is uniformly convex in every direction, then a direct sum
of X and Y, with respect to a strictly monotone norm, has the weak fixed
point property. The result is new even if Y is a finite-dimensional space.
Archive classification: math.FA
Remarks: 9 pages. To appear, Studia Mathematica
Submitted from: awisnic at golem.umcs.lublin.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.6965
or
http://arXiv.org/abs/1111.6965
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Ron Blei
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:39:47 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "The Grothendieck inequality
revisited" by Ron Blei.
Abstract: The classical Grothendieck inequality is viewed as a statement
about representations of functions of two variables over discrete domains
by integrals of two-fold products of functions of one variable. An
analogous statement is proved, concerning continuous functions of two
variables over general topological domains.
The main result is a representation of the inner product in a Hilbert
space by an integral with uniformly bounded and continuous integrands. The
Parseval-like formula is obtained by iterating the usual Parseval
formula in a framework of harmonic analysis on dyadic groups. A modified
construction implies a similar integral representation of the dual action
between $l^p$ and $l^q$, \ $\frac{1}{p} + \frac{1}{q} = 1$.
Variants of the Grothendieck inequality are derived in higher
dimensions. These variants involve representations of functions of
$n$ variables in terms of functions of $k$ variables, $0 < k < n.$
Multilinear Parseval-like formulas are obtained, extending the bilinear
formula. The resulting formulas yield multilinear extensions of the
bilinear Grothendieck inequality, and are used to characterize the
feasibility of integral representations of multilinear functionals on a
Hilbert space, within a class of functionals whose kernels are supported
by fractional Cartesian products.
Archive classification: math.FA
Submitted from: blei at math.uconn.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.7304
or
http://arXiv.org/abs/1111.7304
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Valentin Ferenczi and Gilles Godefroy
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:41:12 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Tightness of Banach spaces and
Baire category" by Valentin Ferenczi and Gilles Godefroy.
Abstract: We prove several dichotomies on linear embeddings between Banach
spaces. Given an arbitrary Banach space X with a basis, we show that the
relations of isomorphism and bi-embedding are meager or co-meager on the
Polish set of block-subspaces of X. We relate this result with tightness
and minimality of Banach spaces. Examples and open questions are provided.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 54E52
Remarks: 13 pages
Submitted from: ferenczi at ccr.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.6444
or
http://arXiv.org/abs/1111.6444
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Taras Banakh and Ivan Hetman
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:43:23 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "A ``hidden'' characterization
of approximatively polyhedral convex sets in Banach spaces" by Taras
Banakh and Ivan Hetman.
Abstract: For a Banach space $X$ by $Conv_H(X)$ we denote the space
of non-empty closed convex subsets of $X$, endowed with the Hausdorff
metric. We prove that for any closed convex set $C\subset X$ and its
metric component $H_C=\{A\in Conv_H(X):d_H(A,C)<\infty\}$ in $Conv_H(X)$,
the following conditions are equivalent: (1) $C$ is approximatively
polyhedral, which means that for every $\epsilon>0$ there is a polyhedral
convex subset $P\subset X$ on Hausdorff distance $d_H(P,C)<\epsilon$
from $C$; (2) $C$ lies on finite Hausdorff distance $d_H(C,P)$ from some
polyhedral convex set $P\subset X$; (3) the metric space $(H_C,d_H)$
is separable; (4) $H_C$ has density $dens(H_C)<\mathfrak c$; (5) $H_C$
does not contain a positively hiding convex set $P\subset X$.
If the Banach space $X$ is finite-dimensional, then the conditions
(1)--(5) are equivalent to: (6) $C$ is not positively hiding; (7) $C$ is
not
infinitely hiding.
A convex subset $C\subset X$ is called {\em positively hiding}
(resp. {\em infinitely hiding}) if there is an infinite set $A\subset
X\setminus C$ such that $\inf_{a\in A}dist(a,C)>0$ (resp. $\sup_{a\in
A}dist(a,C)=\infty$) and for any distinct points $a,b\in A$ the segment
$[a,b]$ meets the set $C$.
Archive classification: math.FA math.GN
Mathematics Subject Classification: 46A55, 46N10, 52B05, 52A07, 52A27,
52A37
Remarks: 14 pages
Submitted from: tbanakh at yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.6708
or
http://arXiv.org/abs/1111.6708
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Hossein Dehghan
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:45:03 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Approximating fixed points
of asymptotically nonexpansive mappings in Banach spaces by metric
projections" by Hossein Dehghan.
Abstract: In this paper, a strong convergence theorem for asymptotically
nonexpansive mappings in a uniformly convex and smooth Banach space is
proved by using metric projections. This theorem extends and improves
the recent strong convergence theorem due to Matsushita and Takahashi [
Appl. Math. Comput. 196 (2008) 422-425] which was established for
nonexpansive mappings.
Archive classification: math.FA
Mathematics Subject Classification: 47H09, 47H10
Submitted from: h_dehghan at iasbs.ac.ir
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1111.7107
or
http://arXiv.org/abs/1111.7107
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Stephen Simons
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:46:22 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Linear $q$--positive sets and
their polar subspaces" by Stephen Simons.
Abstract: In this paper, we define a Banach SNL space to be a Banach
space with a certain linear map from it into its dual, and we develop
the theory of $q$--positive linear subsets of Banach SNL spaces with
Banach SNL dual spaces. We use this theory to give simplified proofs
of some recent results of Bauschke, Borwein, Wang and Yao, and also of
the classical Brezis–Browder theorem.
Archive classification: math.FA
Remarks: 11 pages
Submitted from: simons at math.ucsb.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.0280
or
http://arXiv.org/abs/1112.0280
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Yanqi Qiu
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:47:58 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "On the \text{UMD} constants for
a class of iterated $L_p(L_q)$ spaces" by Yanqi Qiu.
Abstract: Let $1 < p \neq q < \infty$ and $(D, \mu) = (\{\pm 1\},
\frac{1}{2} \delta_{-1} + \frac{1}{2}\delta_1)$. Define by recursion: $X_0
= \C$ and $X_{n+1} = L_p(\mu; L_q(\mu; X_n))$. In this paper, we show that
there exist $c_1=c_1(p, q)>1$ and $ c_2 = c_2(p, q, s) > 1$, such that
the $\text{UMD}_s$ constants of $X_n$'s satisfy $c_1^n \leq C_s(X_n) \leq
c_2^n$ for all $1 < s < \infty$. Similar results will be showed for the
analytic $\text{UMD}$ constants. We mention that the first super-reflexive
non-$\text{UMD}$ Banach lattices were constructed by Bourgain. Our results
yield another elementary construction of super-reflexive non-$\text{UMD}$
Banach lattices, i.e. the inductive limit of $X_n$, which can be viewed
as iterating infinitely many times $L_p(L_q)$.
Archive classification: math.FA
Remarks: 18 pages
Submitted from: yqi.qiu at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.0739
or
http://arXiv.org/abs/1112.0739
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Mikhail I. Ostrovskii
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:49:34 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Different forms of metric
characterizations of classes of Banach spaces" by Mikhail I. Ostrovskii.
Abstract: For each sequence X of finite-dimensional Banach spaces there
exists a sequence H of finite connected nweighted graphs with maximum
degree 3 such that the following conditions on a Banach space Y are
equivalent: (1) Y admits uniformly isomorphic embeddings of elements of
the sequence X. (2) Y admits uniformly bilipschitz embeddings of elements
of the sequence H.
Archive classification: math.FA math.CO math.MG
Mathematics Subject Classification: Primary: 46B07, Secondary: 05C12,
46B85, 54E35
Remarks: Accepted for publication in Houston Journal of Mathematics
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.0801
or
http://arXiv.org/abs/1112.0801
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by D. Azagra
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:53:26 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Global approximation of convex
functions" by D. Azagra.
Abstract: We show that for every (not necessarily bounded) open convex
subset $U$ of $\R^n$, every (not necessarily Lipschitz or strongly)
convex function $f:U\to\R$ can be approximated by real analytic convex
functions, uniformly on all of $U$. In doing so we provide a technique
which transfers results on uniform approximation on bounded sets to
results on uniform approximation on unbounded sets, in such a way that not
only convexity and $C^k$ smoothness, but also local Lipschitz constants,
minimizers, order, and strict or strong convexity, are preserved. This
transfer method is quite general and it can also be used to obtain
new results on approximation of convex functions defined on Riemannian
manifolds or Banach spaces. We also provide a characterization of the
class of convex functions which can be uniformly approximated on $\R^n$
by strongly convex functions.
Archive classification: math.FA math.CA math.DG
Mathematics Subject Classification: 26B25, 41A30, 52A1, 46B20, 49N99,
58E99
Remarks: 16 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/1112.1042
or
http://arXiv.org/abs/1112.1042
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Konstantin Storozhuk
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:55:02 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Strongly normal cones and the
midpoint locally uniform rotundity" by Konstantin Storozhuk.
Abstract: We give the method of construction of normal but not strongly
normal positive cones in Banach space.
Archive classification: math.FA
Mathematics Subject Classification: 46B40
Remarks: 5 pages, 3 figures
Submitted from: stork at math.nsc.ru
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.1196
or
http://arXiv.org/abs/1112.1196
Return-path: <alspach at math.okstate.edu>
Subject: Abstract of a paper by Marcel de Jeu and Marten Wortel
From: alspach at math.okstate.edu (Dale Alspach)
Date: Tue, 20 Dec 2011 10:56:36 -0600 (CST)
To: alspach at math.okstate.edu, banach at math.okstate.edu
This is an announcement for the paper "Compact groups of positive
operators on Banach lattices" by Marcel de Jeu and Marten Wortel.
Abstract: In this paper we study groups of positive operators on Banach
lattices. If a certain factorization property, for which we are not
aware of counterexamples, holds for the elements of such a group, the
group has a homomorphic image in the isometric positive operators which
has the same invariant ideals as the original group. If the group is
compact in the strong operator topology, it equals a group of isometric
positive operators conjugated by a single central lattice automorphism,
provided an additional technical assumption is satisfied, for which
we again have only examples. We obtain a characterization of positive
representations of a group with compact image in the strong operator
topology, and use this for normalized symmetric Banach sequence spaces
to prove an ordered version of the decomposition theorem for unitary
representations of compact groups. Applications concerning spaces of
continuous functions are also considered.
Archive classification: math.FA math.RT
Mathematics Subject Classification: Primary 22D12, Secondary 22C05, 46B42
Remarks: 21 pages
Submitted from: marten.wortel at gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.1611
or
http://arXiv.org/abs/1112.1611
Return-path: <alspach at math.okstate.edu>
Subject: [Banach] Kalton memorial website
To: banach at math.okstate.edu
Date: Wed, 28 Dec 2011 18:46:31 -0600
From: Dale Alspach <alspach at math.okstate.edu>
Dear Colleagues,
The Memorial website in honor of Nigel Kalton is now active:
http://kaltonmemorial.missouri.edu/
The website is not entirely finished yet, in the end we expect nearly
all (perhaps, all) of his publications freely available as pdf files.
We welcome additional contributions such as, photos, stories,
reminiscences, etc. In particular, we hope to receive more contributions
describing various aspects of Nigel's work.
Please send all material to
Fritz Gesztesy
Department of Mathematics
University of Missouri
Columbia, MO 65211
USA
E-mail: gesztesyf at missouri.edu
Best regards,
Fritz Gesztesy
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 08:56:53 CST
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 Tal Orenshtein and Boaz Tsaban
This is an announcement for the paper "Pointwise convergence of partial
functions: The Gerlits-Nagy Problem" by Tal Orenshtein and Boaz Tsaban.
Abstract: For a set X of real numbers, let B(X) denote the space of
Borel real-valued functions on $X$, with the topology inherited from the
Tychonoff product R^X. Assume that for each countable subset A of B(X),
each f in the closure of A is in the closure of $A$ under pointwise
limits of sequences of partial functions. We show that in this case,
B(X) is countably Frechet-Urysohn, that is, each point in the closure of
a countable set is a limit of a sequence of elements of that set. This
solves a problem of Arnold Miller. The continuous version of this
problem is equivalent to a notorious open problem of Gerlits and Nagy.
Answering a question of Salvador Hernandez, we show that the same result
holds for the space of all Baire class 1 functions on X.
We conjecture that the answer to the continuous version of this
problem is negative, but we identify a nontrivial class of sets X of real
numbers, for which we can provide a positive solution to this problem.
The proofs establish new local-to-global correspondences, and use
methods of infinite-combinatorial topology, including a new fusion result
of Francis Jordan.
Archive classification: math.GN math.CA math.CO math.FA math.LO
Remarks: Submitted for publication
Submitted from: tsaban at math.biu.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.2373
or
http://arXiv.org/abs/1112.2373
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 08:58:53 CST
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 Valentin Ferenczi and Thomas Schlumprecht
This is an announcement for the paper "Subsequential minimality in Gowers
and Maurey spaces" by Valentin Ferenczi and Thomas Schlumprecht.
Abstract: We define block sequences $(x_n)$ in every block subspace of a
variant of the space of Gowers and Maurey so that the map $x_{2n-1}\mapsto
x_{2n} $ extends to an isomorphism. This implies the existence of a
subsequentially minimal HI space, which solves a question in \cite{FR}.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 03E15
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/1112.2411
or
http://arXiv.org/abs/1112.2411
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:00:36 CST
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 Andrea Colesanti and Ilaria Fragala
This is an announcement for the paper "The area measure of log-concave
functions and related inequalities" by Andrea Colesanti and Ilaria
Fragala.
Abstract: On the class of log-concave functions on $\R^n$, endowed with a
suitable algebraic structure, we study the first variation of the total
mass functional, which corresponds to the volume of convex bodies when
restricted to the subclass of characteristic functions. We prove some
integral representation formulae for such first variation, which lead
to define in a natural way the notion of area measure for a log-concave
function. In the same framework, we obtain a functional counterpart
of Minkowski first inequality for convex bodies; as corollaries, we
derive a functional form of the isoperimetric inequality, and a family
of logarithmic-type Sobolev inequalities with respect to log-concave
probability measures. Finally, we propose a suitable functional version
of the classical Minkowski problem for convex bodies, and prove some
partial results towards its solution.
Archive classification: math.FA math.MG
Remarks: 36 pages
Submitted from: colesant at math.unifi.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.2555
or
http://arXiv.org/abs/1112.2555
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:02:34 CST
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 Guixiang Hong and Zhi Yin
This is an announcement for the paper "Wavelet approach to operator-valued
Hardy spaces" by Guixiang Hong and Zhi Yin.
Abstract: This paper is devoted to the study of operator-valued
Hardy spaces via wavelet method. This approach is parallel to that in
noncommutative martingale case. We show that our Hardy spaces defined
by wavelet coincide with those introduced by Tao Mei via the usual
Lusin and Littlewood-Paley square functions. As a consequence, we give
an explicit complete unconditional basis of the Hardy space H1(R) when
H1(R) is equipped with an appropriate operator space structure.
Archive classification: math.FA math.CA
Submitted from: ghong at univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.2912
or
http://arXiv.org/abs/1112.2912
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:05:01 CST
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 Steven Heilman, Aukosh Jagannath, and Assaf
Naor
This is an announcement for the paper "Solution of the propeller
conjecture in $\R^3$" by Steven Heilman, Aukosh Jagannath, and Assaf Naor.
Abstract: It is shown that every measurable partition $\{A_1,\ldots,
A_k\}$ of $\R^3$ satisfies
\begin{equation}\label{eq:abs} \sum_{i=1}^k\left\|\int_{A_i}
xe^{-\frac12\|x\|_2^2}dx\right\|_2^2\le 9\pi^2. \end{equation}
Let $\{P_1,P_2,P_3\}$ be the partition of $\R^2$ into $120^\circ$
sectors centered at the origin. The bound~\eqref{eq:abs} is sharp,
with equality holding if $A_i=P_i\times \R$ for $i\in \{1,2,3\}$
and $A_i=\emptyset$ for $i\in \{4,\ldots,k\}$ (up to measure
zero corrections, orthogonal transformations and renumbering
of the sets $\{A_1,\ldots,A_k\}$). This settles positively
the $3$-dimensional Propeller Conjecture of Khot and Naor (FOCS
2008). The proof of~\eqref{eq:abs} reduces the problem to a finite
set of numerical inequalities which are then verified with full rigor
in a computer-assisted fashion. The main consequence (and motivation)
of~\eqref{eq:abs} is complexity-theoretic: the Unique Games hardness
threshold of the Kernel Clustering problem with $4\times 4$ centered
and spherical hypothesis matrix equals $\frac{2\pi}{3}$.
Archive classification: cs.DS math.FA math.MG
Submitted from: naor at cims.nyu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.2993
or
http://arXiv.org/abs/1112.2993
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:08:18 CST
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 Mikhail I. Ostrovskii
This is an announcement for the paper "Test-space characterizations of
some classes of Banach spaces" by Mikhail I. Ostrovskii.
Abstract: Let $\mathcal{P}$ be a class of Banach spaces and let
$T=\{T_\alpha\}_{\alpha\in A}$ be a set of metric spaces. We say that
$T$ is a set of {\it test-spaces} for $\mathcal{P}$ if the following
two conditions are equivalent: (1) $X\notin\mathcal{P}$; (2) The spaces
$\{T_\alpha\}_{\alpha\in A}$ admit uniformly bilipschitz embeddings
into $X$.
The first part of the paper is devoted to a simplification of the
proof of the following test-space characterization obtained in
M.I. Ostrovskii [Different forms of metric characterizations of classes
of Banach spaces, Houston J. Math., to appear]:
For each sequence $\{X_m\}_{m=1}^\infty$ of finite-dimensional Banach
spaces there is a sequence $\{H_n\}_{n=1}^\infty$ of finite connected
unweighted graphs with maximum degree $3$ such that the following
conditions on a Banach space $Y$ are equivalent:
(A) $Y$ admits uniformly isomorphic embeddings of
$\{X_m\}_{m=1}^\infty$;
(B) $Y$ admits uniformly bilipschitz embeddings
of $\{H_n\}_{n=1}^\infty$.
The second part of the paper is devoted
to the case when $\{X_m\}_{m=1}^\infty$ is an increasing sequence of
spaces. It is shown that in this case the class of spaces given by (A)
can be characterized using one test-space, which can be chosen to be an
infinite graph with maximum degree 3.
Archive classification: math.FA math.CO math.MG
Mathematics Subject Classification: Primary: 46B07, Secondary: 05C12,
46B85, 54E35
Submitted from: ostrovsm at stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.3086
or
http://arXiv.org/abs/1112.3086
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:10:02 CST
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 Martin Rmoutil
This is an announcement for the paper "Sigma-porosity is separably
determined" by Marek Cuth and Martin Rmoutil.
Abstract: We prove a separable reduction theorem for sigma-porosity of
Suslin sets. In particular, if A is a Suslin subset in a Banach space X,
then each separable subspace of X can be enlarged to a separable subspace
V such that A is sigma-porous in X if and only if the intersection of A
and V is sigma-porous in V. Such a result is proved for several types
of sigma-porosity. The proof is done using the method of elementary
submodels, hence the results can be combined with other separable
reduction theorems. As an application we extend a theorem of L.Zajicek
on differentiability of Lipschitz functions on separable Asplund spaces
to the nonseparable setting.
Archive classification: math.FA
Mathematics Subject Classification: 28A05, 54E35, 58C20
Submitted from: cuthm5am at karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.3813
or
http://arXiv.org/abs/1112.3813
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:11:57 CST
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 Manor Mendel and Assaf Naor
This is an announcement for the paper "Ultrametric skeletons" by Manor
Mendel and Assaf Naor.
Abstract: We prove that for every $\epsilon\in (0,1)$ there exists
$C_\epsilon\in (0,\infty)$ with the following property. If $(X,d)$ is
a compact metric space and $\mu$ is a Borel probability measure on $X$
then there exists a compact subset $S\subseteq X$ that embeds into an
ultrametric space with distortion $O(1/\epsilon)$, and a probability
measure $\nu$ supported on $S$ satisfying $\nu\left(B_d(x,r)\right)\le
\left(\mu(B_d(x,C_\epsilon r)\right)^{1-\epsilon}$ for all $x\in X$
and $r\in (0,\infty)$. The dependence of the distortion on $\epsilon$
is sharp. We discuss an extension of this statement to multiple measures,
as well as how it implies Talagrand's majorizing measures theorem.
Archive classification: math.MG math.FA math.PR
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/1112.3416
or
http://arXiv.org/abs/1112.3416
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:13:31 CST
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 Fedor Nazarov, Dmitry Ryabogin and Artem
Zvavitch
This is an announcement for the paper "Non-uniqueness of convex bodies
with prescribed volumes of sections and projections" by Fedor Nazarov,
Dmitry Ryabogin and Artem Zvavitch.
Abstract: We show that if $d\ge 4$ is even, then one can find two
essentially different convex bodies such that the volumes of their maximal
sections, central sections, and projections coincide for all directions.
Archive classification: math.CA math.FA math.MG
Mathematics Subject Classification: Primary: 52A20, 52A40, secondary:
52A38
Submitted from: zvavitch at math.kent.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.3976
or
http://arXiv.org/abs/1112.3976
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:15:16 CST
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 Antonio Aviles and Piotr Koszmider
This is an announcement for the paper "A continuous image of a
Radon-Nikod\'{y}m compact which is not Radon-Nikod\'{y}m" by Antonio
Aviles and Piotr Koszmider.
Abstract: We construct a continuous image of a Radon-Nikod\'{y}m compact
space which is not Radon-Nikod\'{y}m compact, solving the problem posed
in the 80ties by Isaac Namioka.
Archive classification: math.FA math.GN math.LO
Submitted from: avileslo at um.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.4152
or
http://arXiv.org/abs/1112.4152
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:18:32 CST
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 David Alonso-Gutierrez, C. Hugo Jimenez,
and Rafael Villa
This is an announcement for the paper "Brunn-Minkowski and Zhang
inequalities for convolution bodies" by David Alonso-Gutierrez, C. Hugo
Jimenez, and Rafael Villa.
Abstract: A quantitative version of Minkowski sum, extending the
definition of $\theta$-convolution of convex bodies, is studied to obtain
extensions of the Brunn-Minkowski and Zhang inequalities, as well as,
other interesting properties on Convex Geometry involving convolution
bodies or polar projection bodies. The extension of this new version to
more than two sets is also given.
Archive classification: math.FA
Mathematics Subject Classification: 52A40 (Primary), 52A20, 52A23
(Secondary)
Remarks: 16 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/1112.4757
or
http://arXiv.org/abs/1112.4757
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:23:26 CST
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. Hugo Jimenez, Marton Naszodi, and Rafael
Villa
This is an announcement for the paper "Push forward measures and
concentration phenomena" by C. Hugo Jimenez, Marton Naszodi, and Rafael
Villa.
Abstract: In this note we study how a concentration phenomenon can be
transmitted from one measure $\mu$ to a push-forward measure $\nu$. In
the first part, we push forward $\mu$ by $\pi:supp(\mu)\rightarrow
\Ren$, where $\pi x=\frac{x}{\norm{x}_L}\norm{x}_K$, and obtain a
concentration inequality in terms of the medians of the given norms
(with respect to $\mu$) and the Banach-Mazur distance between them. This
approach is finer than simply bounding the concentration of the push
forward measure in terms of the Banach-Mazur distance between $K$ and
$L$. As a corollary we show that any normed probability space with good
concentration is far from any high dimensional subspace of the cube. In
the second part, two measures $\mu$ and $\nu$ are given, both related
to the norm $\norm{\cdot}_L$, obtaining a concentration inequality in
which it is involved the Banach-Mazur distance between $K$ and $L$ and the
Lipschitz constant of the map that pushes forward $\mu$ into $\nu$. As an
application, we obtain a concentration inequality for the cross polytope
with respect to the normalized Lebesgue measure and the $\ell_1$ norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B06, 46b07, 46B09, 52A20
Remarks: 12 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/1112.4765
or
http://arXiv.org/abs/1112.4765
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:24:46 CST
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 Serap Oztop and Nico Spronk
This is an announcement for the paper "Minimal and maximal $p$-operator
space structures" by Serap Oztop and Nico Spronk.
Abstract: We show that for $p$-operator spaces, there are natural notions
of minimal and maximal structures. This are useful for dealing with
tensor products.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46L07, 47L25, 46G10
Remarks: 9 pages
Submitted from: nspronk at math.uwaterloo.ca
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.4884
or
http://arXiv.org/abs/1112.4884
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:26:15 CST
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 Deping Ye
This is an announcement for the paper "Inequalities for general mixed
affine surface areas" by Deping Ye.
Abstract: Several general mixed affine surface areas are introduced. We
prove some important properties, such as, affine invariance, for
these general mixed affine surface areas. We also establish new
Alexandrov-Fenchel type inequalities, Santal\'{o}-type inequalities,
and affine isoperimetric inequalities for these general mixed affine
surface areas.
Archive classification: math.MG 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/1112.5129
or
http://arXiv.org/abs/1112.5129
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:31:27 CST
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 Tomasz Kania and Niels Jakob Laustsen
This is an announcement for the paper "Uniqueness of the maximal ideal of
the Banach algebra of bounded operators on $C([0,\omega_1])$" by Tomasz
Kania and Niels Jakob Laustsen.
Abstract: Let $\omega_1$ be the first uncountable ordinal. By a result
of Rudin, bounded operators on the Banach space $C([0,\omega_1])$ have a
natural representation as $[0,\omega_1]\times 0,\omega_1]$-matrices. Loy
and Willis observed that the set of operators whose final
column is continuous when viewed as a scalar-valued function on
$[0,\omega_1]$ defines a maximal ideal of codimension one in the
Banach algebra $\mathscr{B}(C([0,\omega_1]))$ of bounded operators on
$C([0,\omega_1])$. We give a coordinate-free characterization of this
ideal and deduce from it that $\mathscr{B}(C([0,\omega_1]))$ contains
no other maximal ideals. We then obtain a list of equivalent conditions
describing the strictly smaller ideal of operators with separable range,
and finally we investigate the structure of the lattice of all closed
ideals of $\mathscr{B}(C([0,\omega_1]))$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 47L10, 46H10, Secondary 47L20,
46B26, 47B38
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/1112.4800
or
http://arXiv.org/abs/1112.4800
Return-path: <alspach at math.okstate.edu>
Date: Thu, 29 Dec 2011 09:35:21 CST
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 H. G. Dales and M. E. Polyakov
This is an announcement for the paper "Multi-normed spaces" by H. G. Dales
and M. E. Polyakov.
Abstract: We modify the very well known theory of normed spaces $(E,
\norm)$ within functional analysis by considering a sequence $(\norm_n :
n\in\N)$ of norms, where $\norm_n$ is defined on the product space $E^n$
for each $n\in\N$.
Our theory is analogous to, but distinct from, an existing theory of
`operator spaces'; it is designed to relate to general spaces $L^p$
for $p\in [1,\infty]$, and in particular to $L^1$-spaces, rather than
to $L^2$-spaces.
After recalling in Chapter 1 some results in functional analysis,
especially in Banach space, Hilbert space, Banach algebra, and Banach
lattice theory that we shall use, we shall present in Chapter 2 our
axiomatic definition of a `multi-normed space' $((E^n, \norm_n) : n\in
\N)$, where $(E, \norm)$ is a normed space. Several different, equivalent,
characterizations of multi-normed spaces are given, some involving the
theory of tensor products; key examples of multi-norms are the minimum
and maximum multi-norm based on a given space. Multi-norms measure
`geometrical features' of normed spaces, in particular by considering
their `rate of growth'. There is a strong connection between multi-normed
spaces and the theory of absolutely summing operators.
A substantial number of examples of multi-norms will be presented.
Following the pattern of standard presentations of the foundations of
functional analysis, we consider generalizations to `multi-topological
linear spaces' through `multi-null sequences', and to `multi-bounded'
linear operators, which are exactly the `multi-continuous' operators. We
define a new Banach space ${\mathcal M}(E,F)$ of multi-bounded operators,
and show that it generalizes well-known spaces, especially in the theory
of Banach lattices.
We conclude with a theory of `orthogonal decompositions' of a normed
space with respect to a multi-norm, and apply this to construct a
`multi-dual' space.
Archive classification: math.FA
Submitted from: matt.daws at cantab.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1112.5148
or
http://arXiv.org/abs/1112.5148
Return-path: <alspach at math.okstate.edu>
From: "Casazza, Peter" <casazzap at missouri.edu>
To: "banach at math.okstate.edu" <banach at math.okstate.edu>
Date: Thu, 29 Dec 2011 16:56:11 +0000
Subject: [Banach] Nigel Kalton
Dear Friends of Nigel:
The Notices of the AMS is having a special section on
Nigel Kalton. I need pictures of Nigel lecturing at meetings
or with other mathematicians for this issue. If you send
pictures, make it clear who the individuals are and where and when
the picture was taken and any other pertinent information.
I thank you in advance,
Pete Casazza
casazzap at missouri.edu
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