Banach March 2004

banach@mathdept.okstate.edu

3 participants
5 discussions

Informal Analysis Seminar at Kent State
by Dale Alspach 29 Mar '04

29 Mar '04

Despite numerous requests, we are proud to announce the next INFORMAL ANALYSIS SEMINAR KENT STATE UNIVERSITY SATURDAY, APRIL 10, 2004 Speakers: Sergei Treil, Brown University Structured norms, robust control and singular integral operators, Alex Solynin, University of Arkansas, Overdetermined boundary-value problems, quadrature identities, and applications, Igor Pritsker, Oklahoma State University Norms of products of polynomials and a distance function, As usual, the proceedings will commence at noon in the Mathematics Building with a truly gourmet luncheon. We can help arrange accommodation, etc. All are welcome. V. Andriyevskyy, R. Aron, J. Diestel, P. Enflo, V. Gurariy, V. Lomonosov, A. Tonge

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Workshop at A&M
by Bill Johnson 24 Mar '04

24 Mar '04

Workshop in Linear Analysis and Probability Department of Mathematics Texas A&M University Summer 2004 The Summer 2004 session of the Workshop in Linear Analysis and Probability at Texas A&M University will be in session from July 19 until August 14. SUMIRFAS will be held August 6-8. For information about the Workshop, consult the Workshop Home Page, URL http://www.math.tamu.edu/research/workshops/linanalysis/ Ken Dykemma and Gilles Pisier are organizing a Concentration Week on Free Probability Theory and Noncommutative L_p Spaces that will take place August 2-6. The Workshop is supported in part by grants from the National Science Foundation. Limited support for local expenses is available. For logistical help, including requests for support, please contact Cheryl Dorn (cherylr(a)math.tamu.edu). For more information on the Workshop itself, please contact William Johnson (johnson(a)math.tamu.edu), David Larson (larson(a)math.tamu.edu), Gilles Pisier (pisier(a)math.tamu.edu), or Joel Zinn (jzinn(a)math.tamu.edu). For information about the Concentration Week, please contact Ken Dykema (kdykema(a)math.tamu.edu) or Gilles Pisier (pisier(a)math.tamu.edu).

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Abstract of a paper by Roman Vershynin
by Dale Alspach 22 Mar '04

22 Mar '04

This is an announcement for the paper "Integer cells in convex sets" by Roman Vershynin. Abstract: Every convex body K in R^n admits a coordinate projection PK that contains at least vol(0.1 K) cells of the integer lattice PZ^n, provided this volume is at least one. Our proof of this counterpart of Minkowski's theorem is based on an extension of the combinatorial density theorem of Sauer, Shelah and Vapnik-Chervonenkis to Z^n. This leads to a new approach to sections of convex bodies.In particular, fundamental results of the asymptotic convex geometry such as the Volume Ratio Theorem and Milman's duality of the diameters admit natural versions for coordinate sections. Archive classification: Functional Analysis; Combinatorics Mathematics Subject Classification: 52C07, 46B07, 05D05 Remarks: 26 pages The source file(s), vr.tex: 57558 bytes, is(are) stored in gzipped form as 0403278.gz with size 18kb. The corresponding postcript file has gzipped size 89kb. Submitted from: vershynin(a)math.ucdavis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0403278 or http://arXiv.org/abs/math.FA/0403278 or by email in unzipped form by transmitting an empty message with subject line uget 0403278 or in gzipped form by using subject line get 0403278 to: math(a)arXiv.org.

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Abstract of a paper by Gilles Pisier
by Dale Alspach 16 Mar '04

16 Mar '04

This is an announcement for the paper "Completely bounded maps into certain Hilbertian operator spaces" by Gilles Pisier. Abstract: We prove a factorization of completely bounded maps from a $C^*$-algebra $A$ (or an exact operator space $E\subset A$) to $\ell_2$ equipped with the operator space structure of $(C,R)_\theta$ ($0<\theta<1$) obtained by complex interpolation between the column and row Hilbert spaces. More precisely, if $F$ denotes $\ell_2$ equipped with the operator space structure of $(C,R)_\theta$, then $u:\ A \to F$ is completely bounded iff there are states $f,g$ on $A$ and $C>0$ such that \[ \forall a\in A\quad \|ua\|^2\le C f(a^*a)^{1-\theta}g(aa^*)^{\theta}.\] This extends the case $\theta=1/2$ treated in a recent paper with Shlyakhtenko. The constants we obtain tend to 1 when $\theta \to 0$ or $\theta\to 1$. We use analogues of ``free Gaussian" families in non semifinite von Neumann algebras. As an application, we obtain that, if $0<\theta<1$, $(C,R)_\theta$ does not embed completely isomorphically into the predual of a semifinite von Neumann algebra. Moreover, we characterize the subspaces $S\subset R\oplus C$ such that the dual operator space $S^*$ embeds (completely isomorphically) into $M_*$ for some semifinite von neumann algebra $M$: the only possibilities are $S=R$, $S=C$, $S=R\cap C$ and direct sums built out of these three spaces. We also discuss when $S\subset R\oplus C$ is injective, and give a simpler proof of a result due to Oikhberg on this question. In the appendix, we present a proof of Junge's theorem that $OH$ embeds completely isomorphically into a non-commutative $L_1$-space. The main idea is similar to Junge's, but we base the argument on complex interpolation and Shlyakhtenko's generalized circular systems (or ``generalized free Gaussian"), which somewhat unifies Junge's ideas with those of our work with Shlyakhtenko. Archive classification: Operator Algebras; Functional Analysis Mathematics Subject Classification: 46L07, 46L54, 47L25, 47L50 The source file(s), oh3.suite.09.mars.04.tex: 79910 bytes, is(are) stored in gzipped form as 0403220.gz with size 26kb. The corresponding postcript file has gzipped size 109kb. Submitted from: gip(a)ccr.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.OA/0403220 or http://arXiv.org/abs/math.OA/0403220 or by email in unzipped form by transmitting an empty message with subject line uget 0403220 or in gzipped form by using subject line get 0403220 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge and Javier Parcet
by Dale Alspach 09 Mar '04

09 Mar '04

This is an announcement for the paper "The norm of sums of independent non-commutative random variables in $L_p(\ell_1)$" by Marius Junge and Javier Parcet. Abstract: We investigate the norm of sums of independent vector-valued random variables in non-commutative Lp spaces. This allows us to obtain a uniform family of complete embeddings of the Schatten class Sq^n in Sp(lq^m) with optimal order m=n^2. Using these embeddings we show the surprising fact that the sharp type (cotype) index in the sense of operator spaces for Lp[0,1] is min(p,p') (max(p,p')). Similar techniques are used to show that the operator space notions of B-convexity and K-convexity are equivalent. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46L07; 46L52; 46L53 Remarks: 30 pages The source file(s), Lp1.tex: 107978 bytes, is(are) stored in gzipped form as 0403103.gz with size 29kb. The corresponding postcript file has gzipped size 133kb. Submitted from: javier.parcet(a)uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0403103 or http://arXiv.org/abs/math.FA/0403103 or by email in unzipped form by transmitting an empty message with subject line uget 0403103 or in gzipped form by using subject line get 0403103 to: math(a)arXiv.org.

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Banach March 2004