Banach spaces of bounded Szlenk index
Functional Analysis
2007-06-06 v1
Abstract
For a countable ordinal a we denote by C_a the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by a. We show that each C_a admits a separable, reflexive universal space. We also show that spaces in the class C_{omega^{a*omega}} embed into spaces of the same class with a basis. As a consequence we deduce that each C_a is analytic in the Effros-Borel structure of subspaces of C[0,1].
Keywords
Cite
@article{arxiv.0706.0656,
title = {Banach spaces of bounded Szlenk index},
author = {Edward Odell and Thomas Schlumprecht and András Zsák},
journal= {arXiv preprint arXiv:0706.0656},
year = {2007}
}
Comments
29 pages, uses mypreamble.tex and szlenk.bbl