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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 272, Issue 2, 15 January 2017, Pages 498-521
Journal: Journal of Functional Analysis - Volume 272, Issue 2, 15 January 2017, Pages 498-521
نویسندگان
G. Lancien, A. Procházka, M. Raja,