Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Gilles Pisier
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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

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Abstract of a paper by Boris Rubin
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Tord Sj\"odin
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Enrique A. Sanchez Perez and Dirk Werner
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Vladimir Kadets, Miguel Martin, Javier Meri, and Dirk Werner
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Mikhail I. Ostrovskii
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Mikhail I. Ostrovskii
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Radoslaw Adamczak, Rafal Latala, Alexander E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Pericles D Pavlakos and Minos Petrakis
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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Abstract of a paper by Marek Kosiek and Krzysztof Rudol
by alspach＠math.okstate.edu 21 Mar '11

21 Mar '11

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(a)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

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