A universal reflexive space for the class of uniformly convex Banach spaces Academic Article uri icon

abstract

  • We show that there exists a separable reflexive Banach space into which every separable uniformly convex Banach space isomorphically embeds. This solves problems raised by J. Bourgain [B] in 1980 and by W. B. Johnson in 1977 [Jo]. 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.

author list (cited authors)

  • Odell, E., & Schlumprecht, T. h.

citation count

  • 9

publication date

  • June 2006