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

Author information

Contact details are reproduced from the original publication and may be historical.

Jörg Wenzel

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

wenzel@minet.uni-jena.de

Keywords

  • (Strong) martingale type
  • (strong) martingale cotype
  • uniform convexity
  • uniform smoothness

References

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Suggested citation

J. Wenzel. “Strong Martingale Type and Uniform Smoothness.” Journal of Convex Analysis 12 (2005), No. 1, 159–171. https://doi.org/10.68381/jca12011

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.