This is an announcement for the paper "A universal reflexive space for the class of uniformly convex Banach spaces" by E. Odell and 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.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B03; secondary 46B20

Remarks: 13 pages, amslatex

The source file(s), os-universal2-archive.tex: 45823 bytes, is(are) stored in gzipped form as 0507509.gz with size 14kb. The corresponding postcript file has gzipped size 78kb.

Submitted from: combs@mail.ma.utexas.edu

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