Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774758 | Journal of Mathematical Analysis and Applications | 2017 | 20 Pages |
Abstract
Let X be a Banach space with an 1-unconditional Schauder basis and without isomorphic copies of â1âc0. 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:CâC 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
T. DomÃnguez Benavides, M.A. Japón,