Banach spaces of bounded Szlenk index Academic Article uri icon

abstract

  • For a countable ordinal α we denote by Cα, the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each Cα, admits a separable, reflexive universal space. We also show that spaces in the class Cωα·ω embed into spaces of the same class with a basis. As a consequence we deduce that each Cα is analytic in the Effros-Borel structure of subspaces of C[0, 1]. © Instytut Matematyczny PAN, 2007.

author list (cited authors)

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

citation count

  • 16

publication date

  • January 2007