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

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

2005-07-25

arxiv.org/abs/math/0507509v2

Math. Ann. 335 (2006), no. 4, 901--916

Mathematics

Functional Analysis

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

Scientific paper

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.

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