Banach February 2008

banach@mathdept.okstate.edu

2 participants
23 discussions

Abstract of a paper by Mark Rudelson and Roman Vershynin
by alspach＠fourier.math.okstate.edu 29 Feb '08

29 Feb '08

This is an announcement for the paper "The smallest singular value of a random rectangular matrix" by Mark Rudelson and Roman Vershynin. Abstract: We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N by n matrix A with independent and identically distributed subgaussian entries, the smallest singular value of A is at least of the order \sqrt{N} - \sqrt{n-1} with high probability. A sharp estimate on the probability is also obtained. Archive classification: math.PR math.FA Mathematics Subject Classification: 15A52, 11P70 Remarks: 32 pages The source file(s), rv-rectangular-matrices.tex: 80875 bytes, is(are) stored in gzipped form as 0802.3956.gz with size 23kb. The corresponding postcript file has gzipped size 149kb. 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/0802.3956 or http://arXiv.org/abs/0802.3956 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3956 or in gzipped form by using subject line get 0802.3956 to: math(a)arXiv.org.

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Abstract of a paper by M.I. Ostrovskii
by alspach＠fourier.math.okstate.edu 27 Feb '08

27 Feb '08

This is an announcement for the paper "Coarse embeddability into Banach spaces" by M.I. Ostrovskii. Abstract: The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse non-embeddability into $\ell_2$ implies presence of expander-like structures? (b) To what extent $\ell_2$ is the most difficult space to embed into? Archive classification: math.FA math.MG Mathematics Subject Classification: 46B20; 54E40 Remarks: 23 pages The source file(s), Coarse2007.tex: 46609 bytes, is(are) stored in gzipped form as 0802.3666.gz with size 15kb. The corresponding postcript file has gzipped size 125kb. Submitted from: ostrovsm(a)stjohns.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3666 or http://arXiv.org/abs/0802.3666 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3666 or in gzipped form by using subject line get 0802.3666 to: math(a)arXiv.org.

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Abstract of a paper by Peng Gao
by alspach＠fourier.math.okstate.edu 27 Feb '08

27 Feb '08

This is an announcement for the paper "On $l^2$ norms of some weighted mean matrices" by Peng Gao. Abstract: We give another proof of a result of Bennett on the $l^{p}$ operator norms of some weighted mean matrices for the case $p=2$. Archive classification: math.FA Mathematics Subject Classification: 47A30 Remarks: 6 pages The source file(s), Bilinearineqarxiv.tex: 25253 bytes, is(are) stored in gzipped form as 0802.3546.gz with size 7kb. The corresponding postcript file has gzipped size 71kb. Submitted from: penggao(a)utsc.utoronto.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3546 or http://arXiv.org/abs/0802.3546 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3546 or in gzipped form by using subject line get 0802.3546 to: math(a)arXiv.org.

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Abstract of a paper by Michael Cwikel
by alspach＠fourier.math.okstate.edu 27 Feb '08

27 Feb '08

This is an announcement for the paper "Complex interpolation of compact operators mapping into lattice couples" by Michael Cwikel. Abstract: Suppose that (A_0,A_1) and (B_0,B_1) are Banach couples, and that T is a linear operator which maps A_0 compactly into B_0 and A_1 boundedly (or even compactly) into B_1. Does this imply that T maps [A_0,A_1]_s to [B_0,B_1]_s compactly for 0<s<1 ? (Here, as usual, [A_0,A_1]_s denotes the complex interpolation space of Alberto Calderon.) This question has been open for 44 years. Affirmative answers are known for it in many special cases. We answer it affirmatively in the case where (A_0,A_1) is arbitrary and (B_0,B_1) is a couple of Banach lattices having absolutely continuous norms or the Fatou property. Archive classification: math.FA Mathematics Subject Classification: 46B70, 46E30 (primary) Remarks: 14 pages. (Page 13 contains routine and standard material which you The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3520 or http://arXiv.org/abs/0802.3520 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3520 or in gzipped form by using subject line get 0802.3520 to: math(a)arXiv.org.

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Abstract of a paper by Yoshimichi Ueda
by alspach＠fourier.math.okstate.edu 26 Feb '08

26 Feb '08

This is an announcement for the paper "On peak phenomena for non-commutative $H^\infty$" by Yoshimichi Ueda. Abstract: A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual, and moreover some of the results of Blecher and Labuschagne are generalized to the complete form. Archive classification: math.FA math.OA The source file(s), peak.tex: 31983 bytes, is(are) stored in gzipped form as 0802.3449.gz with size 10kb. The corresponding postcript file has gzipped size 78kb. Submitted from: ueda(a)math.kyushu-u.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.3449 or http://arXiv.org/abs/0802.3449 or by email in unzipped form by transmitting an empty message with subject line uget 0802.3449 or in gzipped form by using subject line get 0802.3449 to: math(a)arXiv.org.

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Lior Tzafriri
by Dale Alspach 25 Feb '08

25 Feb '08

Lior Tzafriri, Professor Emeritus at the Hebrew University of Jerusalem, died Sunday morning after undergoing heart surgery. Lior had recovered from surgery he underwent in the autumn. He was leading a normal life, going out, frequently coming to the Institute of Mathematics, and was as well humored as usual. Those who knew Lior will miss not only his sharp mathematical insights but his enormous sense of humor, true wisdom, and his gentle behavior that was so surprising for a person with such a strong personality and independence of mind. Lior's funeral will take place 12:00 Tuesday, February 26, at Bet Hahesped, We are very sorry to announce that Professor Lior Tzafriri passed away on February 24, 2008. He died in Jerusalem during an open heart surgery for replacement of a valve in his heart. Lior was born on May 9, 1936 in Bucharest and emigrated to Israel in 1961. He started his university studies in Bucharest but did his PhD in Jerusalem on the subject of spectral operators. He was on the faculty of the Hebrew University since 1970, as a full professor since 1978. He was a visiting professor in several universities, including Northwestern University, University of Minnesota, California Institute of Technology, Cambridge University, University of Copenhagen, IHES, Ohio State University and Texas A&M. Most of his research work was in Banach space theory. Here are some of his contributions to the subject: 1. The solution of the complemented subspaces problem (with J. Lindenstrauss). 2. The structure theory of Orlicz sequence spaces (with J. Lindenstrauss). 3. Spaces with unique unconditional bases up to permutation (with J. Bourgain, P. Casazza and J. Lindenstrauss). 4. The textbooks: Classical Banach Spaces I, II (with J. Lindenstrauss). 5. The 0-2 law (with Y. Katznelson). 6. The structure of Banach spaces with a symmetric structure (with W. B. Johnson, B. Maurey and G. Schechtman). 7. Invertibility of large submatrices (with J. Bourgain). 8. The structure of finite dimensional subspaces of Lp (with J. Bourgain). 9. Work on the Kadison Singer problem (with J. Bourgain). Lior Tzafriri did an outstanding job as the chairman of the Mathematics Department of the Hebrew University during his two separate terms. Those who knew Lior will miss not only his sharp mathematical insights but his enormous sense of humor, true wisdom, and his gentle behavior that was so surprising for a person with such a strong personality and independence of mind. Lior is survived by Marianna, his wife of 51 years; his daughter Edna; his son Rami; and three grandchildren. (Sent by Bill Johnson)

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Abstract of a paper by Heinz H. Bauschke, Xianfu Wang, Jane Ye and Xiaoming Yuan
by alspach＠fourier.math.okstate.edu 22 Feb '08

22 Feb '08

This is an announcement for the paper "Bregman distances and Klee sets" by Heinz H. Bauschke, Xianfu Wang, Jane Ye and Xiaoming Yuan. Abstract: In 1960, Klee showed that a subset of a Euclidean space must be a singleton provided that each point in the space has a unique farthest point in the set. This classical result has received much attention; in fact, the Hilbert space version is a famous open problem. In this paper, we consider Klee sets from a new perspective. Rather than measuring distance induced by a norm, we focus on the case when distance is meant in the sense of Bregman, i.e., induced by a convex function. When the convex function has sufficiently nice properties, then - analogously to the Euclidean distance case - every Klee set must be a singleton. We provide two proofs of this result, based on Monotone Operator Theory and on Nonsmooth Analysis. The latter approach leads to results that complement work by Hiriart-Urruty on the Euclidean case. Archive classification: math.FA math.OC Mathematics Subject Classification: 47H05; 41A65; 49J52 The source file(s), submitted.tex: 49600 bytes, is(are) stored in gzipped form as 0802.2322.gz with size 15kb. The corresponding postcript file has gzipped size 113kb. Submitted from: heinz.bauschke(a)ubc.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.2322 or http://arXiv.org/abs/0802.2322 or by email in unzipped form by transmitting an empty message with subject line uget 0802.2322 or in gzipped form by using subject line get 0802.2322 to: math(a)arXiv.org.

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Abstract of a paper by D.Karayannakis
by alspach＠fourier.math.okstate.edu 22 Feb '08

22 Feb '08

This is an announcement for the paper "On a conjectured inequality in convex analysis in the case of the unit ball of lp^n" by D.Karayannakis. Abstract: We re-confirm one of the recently stated conjectures of G.Kuperberg of significant convex analysis interest and confirmed very recently for the case of the unit p-ball by A.D.Gutierrez(by use of polygamma functions and convexity theory),this time using only the fundamentals of the gamma function and some mild classical analysis tools. Archive classification: math.CA math.FA Remarks: 4 pages,part of these results comprise a poster to be presented at the 5th Congress of European Mathematics, Amsterdam July 2008 The source file(s), ONACONJECTUREDINEQUALITYINCONVEXANALYSISFORTHECA.pdf: 77405 bytes, is(are) stored in gzipped form as 0802.2014.pdf with size 76kb. Submitted from: dkar(a)stef.teiher.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.2014 or http://arXiv.org/abs/0802.2014 or by email in unzipped form by transmitting an empty message with subject line uget 0802.2014 or in gzipped form by using subject line get 0802.2014 to: math(a)arXiv.org.

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Abstract of a paper by Wieslaw Kubis
by alspach＠fourier.math.okstate.edu 22 Feb '08

22 Feb '08

This is an announcement for the paper "Banach spaces with projectional skeletons" by Wieslaw Kubis. Abstract: A projectional skeleton in a Banach space is a sigma-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to Sigma-spaces. We characterize the existence of a projectional skeleton in terms of elementary substructures, providing simple proofs of known results concerning weakly compactly generated spaces and Plichko spaces. We prove a preservation result for Plichko Banach spaces, involving transfinite sequences of projections. As a corollary, we show that a Banach space is Plichko if and only if it has a commutative projectional skeleton. Archive classification: math.FA math.GN Mathematics Subject Classification: 46B26; 46B03; 46E15; 54C35 Remarks: 30 pages (including index and toc), submitted The source file(s), projs_survey-ver2e.bbl: 7090 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.1109 or http://arXiv.org/abs/0802.1109 or by email in unzipped form by transmitting an empty message with subject line uget 0802.1109 or in gzipped form by using subject line get 0802.1109 to: math(a)arXiv.org.

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Abstract of a paper by Matthew Neal and Bernard Russo
by alspach＠fourier.math.okstate.edu 22 Feb '08

22 Feb '08

This is an announcement for the paper "Contractively complemented subspaces of pre-symmetric spaces" by Matthew Neal and Bernard Russo. Abstract: In 1965, Ron Douglas proved that if $X$ is a closed subspace of an $L^1$-space and $X$ is isometric to another $L^1$-space, then $X$ is the range of a contractive projection on the containing $L^1$-space. In 1977 Arazy-Friedman showed that if a subspace $X$ of $C_1$ is isometric to another $C_1$-space (possibly finite dimensional), then there is a contractive projection of $C_1$ onto $X$. In 1993 Kirchberg proved that if a subspace $X$ of the predual of a von Neumann algebra $M$ is isometric to the predual of another von Neumann algebra, then there is a contractive projection of the predual of $M$ onto $X$. We widen significantly the scope of these results by showing that if a subspace $X$ of the predual of a $JBW^*$-triple $A$ is isometric to the predual of another $JBW^*$-triple $B$, then there is a contractive projection on the predual of $A$ with range $X$, as long as $B$ does not have a direct summand which is isometric to a space of the form $L^\infty(\Omega,H)$, where $H$ is a Hilbert space of dimension at least two. The result is false without this restriction on $B$. Archive classification: math.OA math.FA Mathematics Subject Classification: 46B04,46L70,17C65 Remarks: 25 pages The source file(s), ngoz020508.tex: 97855 bytes, is(are) stored in gzipped form as 0802.0734.gz with size 29kb. The corresponding postcript file has gzipped size 155kb. Submitted from: brusso(a)math.uci.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0802.0734 or http://arXiv.org/abs/0802.0734 or by email in unzipped form by transmitting an empty message with subject line uget 0802.0734 or in gzipped form by using subject line get 0802.0734 to: math(a)arXiv.org.

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Banach February 2008