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

E. Odell·Th. Schlumprecht
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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.

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E. Odell, Th. Schlumprecht. 2007-01-03. A universal reflexive space for the class of uniformly convex Banach spaces. https://arxiv.org/abs/math/0507509

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