کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5774758 1413566 2017 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A fixed-point characterization of weak compactness in Banach spaces with unconditional Schauder basis
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A fixed-point characterization of weak compactness in Banach spaces with unconditional Schauder basis
چکیده انگلیسی
Let X be a Banach space with an 1-unconditional Schauder basis and without isomorphic copies of ℓ1⊕c0. We obtain an equivalent condition to weak compactness by means of a fixed-point theorem. Namely: a closed convex bounded subset C of X is weakly compact if and only if every cascading nonexpansive mapping T:C→C has a fixed point. We particularize our results when C is the closed unit ball of the Banach space X, obtaining a new characterization of reflexivity. Note that weak compactness is independent of the underlying equivalent norm and that every Banach space with an unconditional Schauder basis can be renormed to be 1-unconditional.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 454, Issue 1, 1 October 2017, Pages 246-264
نویسندگان
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