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
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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
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uget 0710.5907
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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
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