[Banach] Abstract of a paper by Ryan Causey

This is an announcement for the paper "Estimation of the Szlenk index of Banach spaces via Schreier spaces" by Ryan Causey.

Abstract: For each ordinal $\alpha<\omega_1$, we prove the existence of a space with a basis and Szlenk index $\omega^{\alpha+1}$ which is universal for the class of 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B03, 46B28

Submitted from: rcausey@math.tamu.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1212.5576

or

http://arXiv.org/abs/1212.5576