کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5772274 1413356 2017 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Szlenk indices of convex hulls
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Szlenk indices of convex hulls
چکیده انگلیسی
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 ωα+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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 272, Issue 2, 15 January 2017, Pages 498-521
نویسندگان
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