[Banach] Abstract of a paper by J\"org Wenzel

[Dale Alspach]

This is an announcement for the paper "Strong martingale type and uniform
smoothness" by J\"org Wenzel.


Abstract: We introduce stronger versions of the usual notions of
martingale type p <= 2 and cotype q >= 2 of a Banach space X and show that
these concepts are equivalent to uniform p-smoothness and q-convexity,
respectively. All these are metric concepts, so they depend on the
particular norm in X.
  These concepts allow us to get some more insight into the fine line
  between X
being isomorphic to a uniformly p-smooth space or being uniformly
p-smooth itself.
  Instead of looking at Banach spaces, we consider linear operators
  between
Banach spaces right away. The situation of a Banach space X can be
rediscovered from this by considering the identity map of X.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B04 (Primary); 46B20, 47A63
(Secondary)

Remarks: 11 pages

The source file(s), strong.arxiv.tex: 30219 bytes, is(are) stored in
gzipped form as 0407482.gz with size 8kb. The corresponding postcript
file has gzipped size 56kb.

Submitted from: wenzel at minet.uni-jena.de

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 http://front.math.ucdavis.edu/math.FA/0407482

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 http://arXiv.org/abs/math.FA/0407482

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