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Szlenk indices of convex hulls.
- Source :
-
Journal of Functional Analysis . Jan2017, Vol. 272 Issue 2, p498-521. 24p. - Publication Year :
- 2017
-
Abstract
- We study the general measures of non-compactness defined on subsets of a dual Banach space, their associated derivations and their ω -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 ω α + 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 ω . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 272
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 119463231
- Full Text :
- https://doi.org/10.1016/j.jfa.2016.10.013