Estimation of the Szlenk index of Banach spaces via Schreier spaces
Volume 216 / 2013
Studia Mathematica 216 (2013), 149-178
MSC: Primary 46B03; Secondary 46B20.
DOI: 10.4064/sm216-2-4
Abstract
For each ordinal $\alpha <\omega _1$, we prove the existence of a Banach space with a basis and Szlenk index $\omega ^{\alpha +1}$ which is universal for the class of separable Banach spaces with Szlenk index not exceeding $\omega ^\alpha $. Our proof involves developing a characterization of which Banach spaces embed into spaces with an FDD with upper Schreier space estimates.
