Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772274 | Journal of Functional Analysis | 2017 | 24 Pages |
Abstract
We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their Ï-iterates. We introduce the notions of convexifiable and sublinear measure of non-compactness and investigate the properties of its associated fragment and slice derivations. We apply our results to the Kuratowski measure of non-compactness and to the study of the Szlenk index of a Banach space. As a consequence, we obtain that the Szlenk index and the convex Szlenk index of a separable Banach space are always equal. We also give, for any countable ordinal α, a characterization of the Banach spaces with Szlenk index bounded by Ïα+1 in terms of the existence of an equivalent renorming. This extends a result by Knaust, Odell and Schlumprecht on Banach spaces with Szlenk index equal to Ï.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
G. Lancien, A. Procházka, M. Raja,