Banach July 2005

banach@mathdept.okstate.edu

2 participants
5 discussions

Abstract of a paper by E. Odell and Th. Schlumprecht
by Dale Alspach 26 Jul '05

26 Jul '05

This is an announcement for the paper "A universal reflexive space for the class of uniformly convex Banach spaces" by E. Odell and Th. Schlumprecht. Abstract: We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J.~Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$-Hilbertian and/or a block $p$-Besselian finite dimensional decomposition. Archive classification: Functional Analysis Mathematics Subject Classification: 46B03; secondary 46B20 Remarks: 13 pages, amslatex The source file(s), os-universal2-archive.tex: 45823 bytes, is(are) stored in gzipped form as 0507509.gz with size 14kb. The corresponding postcript file has gzipped size 78kb. Submitted from: combs(a)mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507509 or http://arXiv.org/abs/math.FA/0507509 or by email in unzipped form by transmitting an empty message with subject line uget 0507509 or in gzipped form by using subject line get 0507509 to: math(a)arXiv.org.

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Pictures of Haskell Rosenthal
by Dale Alspach 20 Jul '05

20 Jul '05

Haskell Rosenthal retired from The University of Texas this past fall after a long and distinguished career. Haskell's wife, Gayle Rosenthal, would like to receive copies of any photos or e-photos or discs, anything with photos of Haskell, lecturing, hiking, dancing, drinking, or anything else, including photos of friends or places he's known or been to. She is preparing a video montage to be shown during Haskellfest at Texas A&M University, August 4-5, 2005. e-Photos should be sent to: Gayle Rosenthal <gayle-rosenthal(a)austin.rr.com> Hard copies of photos should be sent to: Gayle Rosenthal 311 Nixon Drive Austin TX 78746

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Abstract of a paper by Hermann Pfitzner
by Dale Alspach 19 Jul '05

19 Jul '05

This is an announcement for the paper "A separable L-embedded Banach space has property (X) and is therefore the unique predual of its dual" by Hermann Pfitzner. Abstract: In this note the following is proved. Separable L-embedded spaces - that is separable Banach spaces which are complemented in their biduals such that the norm between the two complementary subspaces is additive - have property (X) which, by a result of Godefroy and Talagrand, entails uniqueness of the space as a predual. Archive classification: Functional Analysis Mathematics Subject Classification: 46B04, 46B03, 46B20 The source file(s), Property_X.tex: 22448 bytes, is(are) stored in gzipped form as 0507354.gz with size 8kb. The corresponding postcript file has gzipped size 41kb. Submitted from: Hermann.Pfitzner(a)univ-orleans.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507354 or http://arXiv.org/abs/math.FA/0507354 or by email in unzipped form by transmitting an empty message with subject line uget 0507354 or in gzipped form by using subject line get 0507354 to: math(a)arXiv.org.

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Abstract of a paper by Mark Rudelson
by Dale Alspach 04 Jul '05

04 Jul '05

This is an announcement for the paper "Invertibility of random matrices: norm of the inverse" by Mark Rudelson. Abstract: Let A be an n by n matrix, whose entries are independent copies of a centered random variable satisfying the subgaussian tail estimate. We prove that the operator norm of A^{-1} does not exceed Cn^{3/2} with probability close to 1. Archive classification: Functional Analysis Mathematics Subject Classification: 15A52, 46B09 Remarks: 25 pages The source file(s), square-matrix.tex: 58844 bytes, is(are) stored in gzipped form as 0507024.gz with size 18kb. The corresponding postcript file has gzipped size 94kb. Submitted from: rudelson(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507024 or http://arXiv.org/abs/math.FA/0507024 or by email in unzipped form by transmitting an empty message with subject line uget 0507024 or in gzipped form by using subject line get 0507024 to: math(a)arXiv.org.

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Abstract of a paper by Olivier Guedon and Mark Rudelson
by Dale Alspach 04 Jul '05

04 Jul '05

This is an announcement for the paper "L_p moments of random vectors via majorizing measures" by Olivier Guedon and Mark Rudelson. Abstract: For a random vector X in R^n, we obtain bounds on the size of a sample, for which the empirical p-th moments of linear functionals are close to the exact ones uniformly on a given convex body K. We prove an estimate for a general random vector and apply it to several problems arising in geometric functional analysis. In particular, we find a short Lewis type decomposition for any finite dimensional subspace of L_p and study in detail the case of an isotropic log-concave random vector. We also prove a concentration estimate for the empirical moments. The main ingredient of the proof is the construction of an appropriate majorizing measure to bound a certain Gaussian process. Archive classification: Functional Analysis Mathematics Subject Classification: 46B09, 52A21 Remarks: 33 pages The source file(s), gr05-06-16.tex: 72987 bytes, is(are) stored in gzipped form as 0507023.gz with size 21kb. The corresponding postcript file has gzipped size 110kb. Submitted from: rudelson(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0507023 or http://arXiv.org/abs/math.FA/0507023 or by email in unzipped form by transmitting an empty message with subject line uget 0507023 or in gzipped form by using subject line get 0507023 to: math(a)arXiv.org.

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Banach July 2005