- Banach - mathdept.okstate.edu

Abstract of a paper by Jarno Talponen
by alspach＠math.okstate.edu 16 Dec '14

16 Dec '14

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

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Abstract of a paper by Gilles Pisier and Eric Ricard
by alspach＠math.okstate.edu 16 Dec '14

16 Dec '14

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

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Abstract of a paper by Astrid Berg, Lukas Parapatits, Franz E. Schuster, and Manuel Weberndorfer
by alspach＠math.okstate.edu 16 Dec '14

16 Dec '14

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

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Abstract of a paper by Aleksandar Nikolov
by alspach＠math.okstate.edu 16 Dec '14

16 Dec '14

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

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Banach J. Math Anal and Ann. Funct. Anal.
by Dale Alspach 16 Dec '14

16 Dec '14

Duke University Press partners with the Tusi Mathematical Research Group to publish the Annals of Functional Analysis (AFA) and the Banach Journal of Mathematical Analysis (BJMA). In 2015, Duke University Press will begin publishing both journals. AFA, started in 2010, and BJMA, started in 2007, are online-only journals included in the prestigious "Reference List Journals" covered by MathSciNet and indexed by Zentralblatt Math, Scopus and Thomson Reuters (ISI). With the start of their 2015 volumes under the guidance of strong editorial boards, the journals will increase in frequency from two to four issues per year. The journals publish research papers and critical survey articles that focus on, but are not limited to, functional analysis, abstract harmonic analysis and operator theory. AFA and BJMA have rapidly established themselves as providing high-level scholarship that addresses important questions in the study of mathematical analysis. The journals are no longer open access but papers will be freely available in Project Euclid 5 years after publication. As before, they will be available on Project Euclid at http://projecteuclid.org/euclid.bjma [1] and http://projecteuclid.org/euclid.afa [2] Editor-in-chief M. S. Moslehian ===========================================================

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Address Changes
by Dale Alspach 15 Dec '14

15 Dec '14

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

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Abstract of a paper by Gideon Schechtman
by alspach＠math.okstate.edu 27 Nov '14

27 Nov '14

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

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Relations Between Banach Space Theory and Geometric Measure Theory workshop, 08 - 12 June 2015, University of Warwick, UK
by Olga Maleva 27 Nov '14

27 Nov '14

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.

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Abstract of a paper by Tomasz Kobos
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

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

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Abstract of a paper by Jorge Tomas Rodriguez
by alspach＠math.okstate.edu 26 Nov '14

26 Nov '14

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

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