Banach November 2007

banach@mathdept.okstate.edu

1 participants
3 discussions

Abstract of a paper by Haskell P. Rosenthal
by Dale Alspach 04 Nov '07

04 Nov '07

This is an announcement for the paper "Some new characterizations of Banach spaces containing $\ell^1$" by Haskell P. Rosenthal. Abstract: Several new characterizations of Banach spaces containing a subspace isomorphic to $\ell^1$, are obtained. These are applied to the question of when $\ell^1$ embeds in the injective tensor product of two Banach spaces. Archive classification: math.FA Remarks: 27 pages, AMSLaTeX The source file(s), new-char.tex: 120502 bytes, is(are) stored in gzipped form as 0710.5944.gz with size 35kb. The corresponding postcript file has gzipped size 163kb. 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/0710.5944 or http://arXiv.org/abs/0710.5944 or by email in unzipped form by transmitting an empty message with subject line uget 0710.5944 or in gzipped form by using subject line get 0710.5944 to: math(a)arXiv.org.

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Abstract of a paper by David Alonso-Gutierrez
by Dale Alspach 04 Nov '07

04 Nov '07

This is an announcement for the paper "On an extension of the Blaschke-Santalo inequality" by David Alonso-Gutierrez. Abstract: Let $K$ be a convex body and $K^\circ$ its polar body. Call $\phi(K)=\frac{1}{|K||K^\circ|}\int_K\int_{K^\circ}\langle x,y\rangle^2 dxdy$. It is conjectured that $\phi(K)$ is maximum when $K$ is the euclidean ball. In particular this statement implies the Blaschke-Santalo inequality. We verify this conjecture when $K$ is restricted to be a $p$--ball. Archive classification: math.FA Mathematics Subject Classification: 52A20; 52A40; 46B20 Remarks: 7 pages The source file(s), p-balls5.tex: 18249 bytes, is(are) stored in gzipped form as 0710.5907.gz with size 6kb. The corresponding postcript file has gzipped size 65kb. Submitted from: 498220(a)celes.unizar.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0710.5907 or http://arXiv.org/abs/0710.5907 or by email in unzipped form by transmitting an empty message with subject line uget 0710.5907 or in gzipped form by using subject line get 0710.5907 to: math(a)arXiv.org.

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Abstract of a paper by Richard J. Smith
by Dale Alspach 04 Nov '07

04 Nov '07

This is an announcement for the paper "Gruenhage compacta and strictly convex dual norms" by Richard J. Smith. Abstract: We prove that if K is a Gruenhage compact space then C(K)* admits an equivalent, strictly convex dual norm. As a corollary, we show that if X is a Banach space and X* is the |.|-closed linear span of K, where K is a Gruenhage compact in the w*-topology and |.| is equivalent to a coarser, w*-lower semicontinuous norm on X*, then X* admits an equivalent, strictly convex dual norm. We give a partial converse to the first result by showing that if T is a tree, then C(T)* admits an equivalent, strictly convex dual norm if and only if T is a Gruenhage space. Finally, we present some stability properties satisfied by Gruenhage spaces; in particular, Gruenhage spaces are stable under perfect images. Archive classification: math.FA math.GN Mathematics Subject Classification: 46B03; 46B26 The source file(s), arxiv29-10-07.tex: 67073 bytes, is(are) stored in gzipped form as 0710.5396.gz with size 19kb. The corresponding postcript file has gzipped size 112kb. Submitted from: rjs209(a)cam.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0710.5396 or http://arXiv.org/abs/0710.5396 or by email in unzipped form by transmitting an empty message with subject line uget 0710.5396 or in gzipped form by using subject line get 0710.5396 to: math(a)arXiv.org.

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Banach November 2007