Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772454 | Journal of Functional Analysis | 2017 | 35 Pages |
Abstract
Given any Banach space X and any weakâ-compact subset K of Xâ, we compute the Szlenk index of the weakâ-closed, convex hull of K as a function of the Szlenk index of K. Also as an application, we compute the Szlenk index of any injective tensor product of two operators. In particular, we compute the Szlenk index of an injective tensor product XâËεY in terms of Sz(X) and Sz(Y). As another application, we give a complete characterization of those ordinals which occur as the Szlenk index of a Banach space, as well as those ordinals which occur as the Bourgain â1 or c0 index of a Banach space.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ryan M. Causey,