ON THE STRUCTURE OF ASYMPTOTIC lp SPACES Academic Article uri icon

abstract

  • We prove that if X is a separable, reflexive space which is asymptotic lp for some 1 ≤ p ≤ ∞, then X embeds into a reflexive space Z having an asymptotic lp finite-dimensional decomposition (FDD). This result leads to an intrinsic characterization of subspaces of spaces with an asymptotic lp FDD. More general results of this type are also obtained. As a consequence, we prove the existence of universal spaces for certain classes of separable, reflexive and asymptotic lp spaces. © 2007. Published by Oxford University Press. All rights reserved.

author list (cited authors)

  • Odell, E., Schlumprecht, T. h., & Zsak, A.

citation count

  • 8

publication date

  • September 2007