Banach February 2014

banach@mathdept.okstate.edu

3 participants
26 discussions

Abstract of a paper by Domenico Candeloro and Anna Rita Sambucini
by alspach＠math.okstate.edu 05 Feb '14

05 Feb '14

This is an announcement for the paper "Filter convergence and decompositions for vector lattice-valued" by Domenico Candeloro and Anna Rita Sambucini. Abstract: Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the finitely additive case is faced, first assuming uniform $s$-boundedness (without restrictions on the filter), then relaxing this condition but imposing stronger properties on the filter. In order to obtain the last results, a Schur-type convergence theorem is used. Archive classification: math.FA Mathematics Subject Classification: 28B15, 28B05, 06A06, 54F05 Report Number: 0901688 30 jan 2014 Remarks: 18 pages Submitted from: anna.sambucini(a)unipg.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.7818 or http://arXiv.org/abs/1401.7818

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Abstract of a paper by Umut Caglar and Elisabeth M. Werner
by alspach＠math.okstate.edu 05 Feb '14

05 Feb '14

This is an announcement for the paper "Mixed f-divergence and inequalities for log concave functions" by Umut Caglar and Elisabeth M. Werner. Abstract: Mixed f-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log concave functions. Special cases of f-divergences are mixed L_\lambda-affine surface areas for log concave functions. For those, we establish various affine isoperimetric inequalities as well as a vector Blaschke Santalo type inequality. Archive classification: math.FA Submitted from: elisabeth.werner(a)case.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.7065 or http://arXiv.org/abs/1401.7065

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Abstract of a paper by Maria Roginskaya and Michal Wojciechowski
by alspach＠math.okstate.edu 05 Feb '14

05 Feb '14

This is an announcement for the paper "Bounded Approximation Property for Sobolev spaces on simply-connected planar domains" by Maria Roginskaya and Michal Wojciechowski. Abstract: We show that Sobolev space $W^1_1(\Omega)$ of any planar one-connected domain $\Omega$ has the Bounded Approximation property. The result holds independently from the properties of the boundary of $\Omega$. The prove is based on a new decomposition of a planar domain. Archive classification: math.FA Submitted from: maria.roginskaya(a)chalmers.se The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.7131 or http://arXiv.org/abs/1401.7131

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Abstract of a paper by Pierre Youssef
by alspach＠math.okstate.edu 05 Feb '14

05 Feb '14

This is an announcement for the paper "Extractig a basis with fixed block inside a matrix" by Pierre Youssef. Abstract: Given $U$ an $n\times m$ matrix of rank $n$ and $V$ block of columns inside $U$, we consider the problem of extracting a block of columns of rank $n$ which minimize the Hilbert-Schmidt norm of the inverse while preserving the block $V$. This generalizes a previous result of Gluskin-Olevskii, and improves the estimates when given a "good" block $V$. Archive classification: math.FA Submitted from: pierre.youssef(a)univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.6434 or http://arXiv.org/abs/1401.6434

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Abstract of a paper by Cesar Ruiz and Victor M. Sanchez
by alspach＠math.okstate.edu 05 Feb '14

05 Feb '14

This is an announcement for the paper "Nonlinear subsets of functions spaces and spaceability" by Cesar Ruiz and Victor M. Sanchez. Abstract: In this paper, we study the existence of infinite dimensional closed linear subspaces of a rearrangement invariant space on [0,1] every nonzero element of which does not belong to any included rearrangement invariant space of the same class such that the inclusion operator is disjointly strictly singular. We consider Lorentz, Marcinkiewicz and Orlicz spaces. The answer is affirmative for Marcinkiewicz spaces and negative for Lorentz and Orlicz spaces. Also, the same problem is studied for Nakano spaces assuming different hypothesis. Archive classification: math.FA Mathematics Subject Classification: 46E30 Remarks: 11 pages Submitted from: victorms(a)mat.ucm.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.5906 or http://arXiv.org/abs/1401.5906

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Abstract of a paper by Timur Oikhberg and Eugeniu Spinu
by alspach＠math.okstate.edu 05 Feb '14

05 Feb '14

This is an announcement for the paper "Subprojective Banach spaces" by Timur Oikhberg and Eugeniu Spinu. Abstract: A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such us direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces. Archive classification: math.FA Submitted from: spinu(a)ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1401.4231 or http://arXiv.org/abs/1401.4231

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Banach February 2014