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