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@minet.uni-jena.de

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