This is an announcement for the paper "Uniform-to-proper duality of
geometric properties of Banach spaces and their ultrapowers" by Jarno
Talponen.
Abstract:
In this note various geometric properties of a Banach space $X$ are
characterized by means of weaker corresponding geometric properties
involving an ultrapower $X^\mathcal{U}$. The characterizations do not
depend on the particular choice of the free ultrafilter $\mathcal{U}$. For
example, a point $x\in S_X$ is an MLUR point if and only if $j(x)$
(given by the canonical inclusion $j\colon X \to X^\mathcal{U}$) in
$\B_{X^\mathcal{U}}$ is an extreme point; a point $x\in S_X$ is LUR if
and only if $j(x)$ is not contained in any non-degenerate line segment
of $S_{X^\mathcal{U}}$; a Banach space $X$ is URED if and only if there
are no $x,y \in S_{X^\mathcal{U}}$, $x\neq y$, with $x-y \in j(X)$.
Archive classification: math.FA math.LO
Mathematics Subject Classification: 03H05, 46B20, 46M07, 46B10
Submitted from: talponen(a)iki.fi
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.1279
or
http://arXiv.org/abs/1412.1279
This is an announcement for the paper "The non-commutative Khintchine
inequalities for $0<p<1$" by Gilles Pisier and Eric Ricard.
Abstract:
We give a proof of the Khintchine inequalities in non-commutative
$L_p$-spaces for all $0< p<1$. These new inequalities are valid for the
Rademacher functions or Gaussian random variables, but also for more
general sequences, e.g. for the analogues of such random variables in
free probability. We also prove a factorization for operators from
a Hilbert space to a non commutative $L_p$-space, which is new for
$0<p<1$. We end by showing that Mazur maps are H\"older on semifinite
von Neumann algebras.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 2000 MSC 46L51, 46L07, 47L25, 47L20
Submitted from: pisier(a)math.tamu.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.0222
or
http://arXiv.org/abs/1412.0222
This is an announcement for the paper "Log-concavity properties of
Minkowski valuations" by Astrid Berg, Lukas Parapatits, Franz E. Schuster,
and Manuel Weberndorfer.
Abstract:
New Orlicz Brunn-Minkowski inequalities are established for rigid
motion compatible Minkowski valuations of arbitrary degree. These extend
classical log-concavity properties of intrinsic volumes and generalize
seminal results of Lutwak and others. Two different approaches which
refine previously employed techniques are explored. It is shown that
both lead to the same class of Minkowski valuations for which these
inequalities hold. An appendix by Semyon Alesker contains the proof of
a new classification of generalized translation invariant valuations.
Archive classification: math.MG math.DG math.FA
Mathematics Subject Classification: 52A38, 52B45
Submitted from: franz.schuster(a)tuwien.ac.at
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.7891
or
http://arXiv.org/abs/1411.7891
This is an announcement for the paper "Randomized rounding for the
largest $j$-simplex problem" by Aleksandar Nikolov.
Abstract:
The maximum volume $j$-simplex problem asks to compute the
$j$-dimensional simplex of maximum volume inside the convex hull of
a given set of $n$ points in $\mathbb{R}^d$. We give a deterministic
approximation algorithm for this problem which achieves an approximation
ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathsf{NP}$-hard
to approximate within a factor of $2^{cj}$ for some constant $c$. Our
algorithm also approximates the problem of finding the largest determinant
principal $j\times j$ submatrix of a rank $d$ positive semidefinite
matrix, with approximation ratio $e^{j + o(j)}$. We achieve our
approximation by rounding solutions to a generlization of the $D$-optimal
design problem, or, equivalently, the dual of an appropriate smallest
enclosing ellipsoid probelm. Our arguments give a short and simple proof
of a restricted invertibility principle for determinants.
Archive classification: cs.CG cs.DS math.FA
Submitted from: anikolov(a)cs.rutgers.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1412.0036
or
http://arXiv.org/abs/1412.0036
Duke University Press partners with the Tusi Mathematical Research Group
to publish the Annals of Functional Analysis (AFA) and the Banach
Journal of Mathematical Analysis (BJMA). In 2015, Duke University Press
will begin publishing both journals.
AFA, started in 2010, and BJMA, started in 2007, are online-only
journals included in the prestigious "Reference List Journals" covered
by MathSciNet and indexed by Zentralblatt Math, Scopus and Thomson
Reuters (ISI).
With the start of their 2015 volumes under the guidance of strong
editorial boards, the journals will increase in frequency from two to
four issues per year. The journals publish research papers and critical
survey articles that focus on, but are not limited to, functional
analysis, abstract harmonic analysis and operator theory. AFA and BJMA
have rapidly established themselves as providing high-level scholarship
that addresses important questions in the study of mathematical
analysis. The journals are no longer open access but papers will be
freely available in Project Euclid 5 years after publication.
As before, they will be available on Project Euclid at
http://projecteuclid.org/euclid.bjma [1] and
http://projecteuclid.org/euclid.afa [2]
Editor-in-chief
M. S. Moslehian
===========================================================
The Banach list is changing its address. Messages should be sent to
banach(a)mathdept.okstate.edu.
The list location for subscribing or unsubscribing is now
https://www.mathdept.okstate.edu/cgi-bin/mailman/listinfo/banach
The URL for lists of past postings and other information is
https://math.okstate.edu/people/alspach/banach/index.html
My current address alspach(a)math.okstate.edu should continue to work
but banach(a)math.okstate.edu will stop working sometime in the next few
weeks.
Best Wishes for the New Year,
Dale Alspach
This is an announcement for the paper "Three observations regarding
Schatten p classes" by Gideon Schechtman.
Abstract:
The paper contains three results, the common feature of which is
that they deal with the Schatten $p$ class. The first is a presentation of
a new complemented subspace of $C_p$ in the reflexive range (and $p\not=
2$). This construction answers a question of Arazy and Lindestrauss from
1975. The second result relates to tight embeddings of finite dimensional
subspaces of $C_p$ in $C_p^n$ with small $n$ and shows that $\ell_p^k$
nicely embeds into $C_p^n$ only if $n$ is at least proportional to $k$
(and then of course the dimension of $C_p^n$ is at least of order
$k^2$). The third result concerns single element of $C_p^n$ and shows
that for $p>2$ any $n\times n$ matrix of $C_p$ norm one and zero diagonal
admits, for every $\varepsilon>0$, a $k$-paving of $C_p$ norm at most
$\varepsilon$ with $k$ depending on $\varepsilon$ and $p$ only.
Archive classification: math.FA
Mathematics Subject Classification: 47B10, 46B20, 46B28
Submitted from: gideon(a)weizmann.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.4427
or
http://arXiv.org/abs/1411.4427
1st ANNOUNCEMENT OF THE WORKSHOP
Relations Between Banach Space Theory and Geometric Measure Theory
08 - 12 June 2015
University of Warwick
United Kingdom
Plenary speakers include:
Jesus M F Castillo (Universidad de Extremadura)
Gilles Godefroy (Université Paris VI)
William B Johnson (Texas A&M University)
Assaf Naor* (Princeton University)
Mikhail Ostrovskii (St.-John's University)
Gideon Schechtman (Weizmann Institute)
Thomas Schlumprecht (Texas A&M University)
*To be confirmed
The homepage of the workshop is: http://tinyurl.com/BanachGMT
To register please follow the links on the homepage of the workshop.
For further information on the workshop please contact the organisers:
* David Preiss <d dot preiss at warwick dot ac dot uk>
* Olga Maleva <o dot maleva at bham dot ac dot uk>
We expect to be able to cover some expenses for a number of participants. Please read more information on the homepage about the funding.
We ask to register your attendance at the workshop by 15 April 2015.
The Workshop is supported by a European Research Council grant.
This is an announcement for the paper "Hyperplanes of finite-dimensional
normed spaces with the maximal relative projection constant" by
Tomasz Kobos.
Abstract:
The \emph{relative projection constant} $\lambda(Y, X)$ of normed spaces
$Y \subset X$ is defined as $\lambda(Y, X) = \inf \{ ||P|| : P \in
\mathcal{P}(X, Y) \}$, where $\mathcal{P}(X, Y)$ denotes the set of
all continuous projections from $X$ onto $Y$. By the well-known result
of Bohnenblust for every $n$-dimensional normed space $X$ and its
subspace $Y$ of codimension $1$ the inequality $\lambda(Y, X) \leq 2 -
\frac{2}{n}$ holds. The main goal of the paper is to study the equality
case in the theorem of Bohnenblust. We establish an equivalent condition
for the equality $\lambda(Y, X) = 2 - \frac{2}{n}$ and present several
applications. We prove that every three-dimensional space has a subspace
with the projection constant less than $\frac{4}{3} - 0.0007$. This
gives a non-trivial upper bound in the problem posed by Bosznay and
Garay. In the general case, we give an upper bound for the number
of $(n-1)$-dimensional subspaces with the maximal relative projection
constant in terms of the facets of the unit ball of $X$. As a consequence,
every $n$-dimensional normed space $X$ has an $(n-1)$-dimensional
subspace $Y$ with $\lambda(Y, X) < 2-\frac{2}{n}$. This contrasts with
the seperable case in which it is possible that every hyperplane has a
maximal possible projection constant.
Archive classification: math.FA
Mathematics Subject Classification: Primary 41A35, 41A65, 47A30, 52A21
Remarks: 15 pages
Submitted from: tkobos(a)wp.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.6214
or
http://arXiv.org/abs/1411.6214
This is an announcement for the paper "On the norm of products of
polynomials on ultraproduct of Banach spaces" by Jorge Tomas Rodriguez.
Abstract:
The purpose of this article is to study the problem of finding sharp
lower bounds for the norm of the product of polynomials in the
ultraproducts of Banach spaces $(X_i)_{\mathfrak U}$. We show that, under
certain hypotheses, there is a strong relation between this problem and
the same problem for the spaces $X_i$.
Archive classification: math.FA
Submitted from: jtrodrig(a)dm.uba.ar
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1411.5894
or
http://arXiv.org/abs/1411.5894