A universal reflexive space for the class of uniformly convex Banach spaces

E. Odell; Th. Schlumprecht

A universal reflexive space for the class of uniformly convex Banach spaces

Functional Analysis 2007-06-13 v2

Authors: E. Odell , Th. Schlumprecht

Abstract

We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves a problem of J. Bourgain. We also give intrinsic characterizations of separable reflexive Banach spaces which embed into a reflexive space with a block $q$ -Hilbertian and/or a block $p$ -Besselian finite dimensional decomposition.

Keywords

reflexive banach space uniformly convex banach space isomorphic embedding block hilbertian finite dimensional decomposition

Cite

@article{arxiv.math/0507509,
  title  = {A universal reflexive space for the class of uniformly convex Banach spaces},
  author = {E. Odell and Th. Schlumprecht},
  journal= {arXiv preprint arXiv:math/0507509},
  year   = {2007}
}

Comments

v.2 (3 January 2007) 13 pages, amslatex

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