[Banach] Abstract of a paper by J\"org Wenzel
alspach at www.math.okstate.edu
Thu Jul 29 08:49:17 CDT 2004
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
being isomorphic to a uniformly p-smooth space or being uniformly
Instead of looking at Banach spaces, we consider linear operators
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
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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