Banach July 2007

banach@mathdept.okstate.edu

3 participants
15 discussions

Abstract of a paper by V.Yaskin
by Dale Alspach 12 Jul '07

12 Jul '07

This is an announcement for the paper "On strict inclusions in hierarchies of convex bodies" by V.Yaskin. Abstract: Let $\mathcal I_k$ be the class of convex $k$-intersection bodies in $\mathbb{R}^n$ (in the sense of Koldobsky) and $\mathcal I_k^m$ be the class of convex origin-symmetric bodies all of whose $m$-dimensional central sections are $k$-intersection bodies. We show that 1) $\mathcal I_k^m\not\subset \mathcal I_k^{m+1}$, $k+3\le m<n$, and 2) $\mathcal I_l \not\subset \mathcal I_k$, $1\le k<l < n-3$. Archive classification: math.FA Mathematics Subject Classification: 52A20, 52A21, 46B04 Remarks: 10 pages The source file(s), Yaskin.tex: 31833 bytes, is(are) stored in gzipped form as 0707.1471.gz with size 10kb. The corresponding postcript file has gzipped size 82kb. Submitted from: vyaskin(a)math.ou.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0707.1471 or http://arXiv.org/abs/0707.1471 or by email in unzipped form by transmitting an empty message with subject line uget 0707.1471 or in gzipped form by using subject line get 0707.1471 to: math(a)arXiv.org.

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Abstract of a paper by Mikael de la Salle
by Dale Alspach 06 Jul '07

06 Jul '07

This is an announcement for the paper "Equimeasurabily and isometries in noncommutative Lp-spaces" by Mikael de la Salle. Abstract: We prove some noncommutative analogues of a theorem by Rudin and Plotkin about equimeasurability and isometries in L_p-spaces. Let 0<p<\infty, p not an even integer. The main result of this paper states that in the category of unital subspaces of noncommutative probability Lp-spaces, the unital completely isometric maps come from *-isomorphisms of the underlying von Neumann algebras. Unfortunately we are only able to treat the case of bounded operators. Archive classification: math.OA math.FA Mathematics Subject Classification: 46L53; 46L51; 47L05 Remarks: 11 pages The source file(s), article_arxiv.bbl: 2056 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0707.0427 or http://arXiv.org/abs/0707.0427 or by email in unzipped form by transmitting an empty message with subject line uget 0707.0427 or in gzipped form by using subject line get 0707.0427 to: math(a)arXiv.org.

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Abstract of a paper by Marius Junge and Hun Hee Lee
by Dale Alspach 06 Jul '07

06 Jul '07

This is an announcement for the paper "A Maurey type result for operator spaces" by Marius Junge and Hun Hee Lee. Abstract: The little Grothendieck theorem for Banach spaces says that every bounded linear operator between $C(K)$ and $\ell_2$ is 2-summing. However, it is shown in \cite{J05} that the operator space analogue fails. Not every cb-map $v : \K \to OH$ is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem : Every cb-map $v : \K \to OH$ is $(q,cb)$-summing for any $q>2$ and hence admits a factorization $\|v(x)\| \leq c(q) \|v\|_{cb} \|axb\|_q$ with $a,b$ in the unit ball of the Schatten class $S_{2q}$. Archive classification: math.FA math.OA Mathematics Subject Classification: 47L25; 46B07 Remarks: 29 pages The source file(s), MaureyTypeResultOS.tex: 99707 bytes, is(are) stored in gzipped form as 0707.0152.gz with size 25kb. The corresponding postcript file has gzipped size 184kb. Submitted from: lee.hunhee(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0707.0152 or http://arXiv.org/abs/0707.0152 or by email in unzipped form by transmitting an empty message with subject line uget 0707.0152 or in gzipped form by using subject line get 0707.0152 to: math(a)arXiv.org.

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Abstract of a paper by Hun Hee Lee
by Dale Alspach 06 Jul '07

06 Jul '07

This is an announcement for the paper "Tsirelson like operator spaces" by Hun Hee Lee. Abstract: We construct nontrivial examples of weak-$C_p$ ($1\leq p \leq \infty$) operator spaces with the local operator space structure very close to $C_p = [R, C]_{\frac{1}{p}}$. These examples are non-homogeneous Hilbertian operator spaces, and their constructions are similar to that of 2-convexified Tsirelson's space by W. B. Johnson. Archive classification: math.FA math.OA Mathematics Subject Classification: 47L25; 46B07 Remarks: 19 pages The source file(s), TsirelsonLikeOS.tex: 54208 bytes, is(are) stored in gzipped form as 0707.0147.gz with size 13kb. The corresponding postcript file has gzipped size 113kb. Submitted from: lee.hunhee(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0707.0147 or http://arXiv.org/abs/0707.0147 or by email in unzipped form by transmitting an empty message with subject line uget 0707.0147 or in gzipped form by using subject line get 0707.0147 to: math(a)arXiv.org.

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Abstract of a paper by Shin-ichi Ohta
by Dale Alspach 06 Jul '07

06 Jul '07

This is an announcement for the paper "Markov type of Alexandrov spaces of nonnegative curvature" by Shin-ichi Ohta. Abstract: We prove that Alexandrov spaces $X$ of nonnegative curvature have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz continuous map from a subset of $X$ into a 2-uniformly convex Banach space is extended as a Lipschitz continuous map on the entire space $X$. Archive classification: math.MG math.FA Mathematics Subject Classification: 46B20, 53C21, 60J10 Remarks: 16 pages The source file(s), type+.tex: 40468 bytes, is(are) stored in gzipped form as 0707.0102.gz with size 11kb. The corresponding postcript file has gzipped size 103kb. Submitted from: sohta(a)math.kyoto-u.ac.jp The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0707.0102 or http://arXiv.org/abs/0707.0102 or by email in unzipped form by transmitting an empty message with subject line uget 0707.0102 or in gzipped form by using subject line get 0707.0102 to: math(a)arXiv.org.

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Banach July 2007