Banach Spaces of Bounded Szlenk Index II

Abstract

For every $\alpha <{\omega }_1$ we establish the existence of a separable Banach space whose Szlenk index is ${\omega }^{\alpha \omega +1}$ and which is universal for all separable Banach spaces whose Szlenk-index does not exceed ${\omega }^{\alpha \omega }$. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates.

References in corpus (1)

• Embedding into Banach spaces with finite dimensional decompositions