Mosco convergence and reflexivity

Beer, G. and Borwein, Jonathan M. (1990) Mosco convergence and reflexivity. Proceedings of the American Mathematical Society, 109 . pp. 427-436. ISSN 0002-9939

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In this note we aim to show conclusively that Mosco convergence of convex sets and functions and the associated Mosco topology τM are useful notions only in the reflexive setting. Specifically, we prove that each of the following conditions is necessary and sufficient for a Banach space X to be reflexive: (1) whenever A , A₁, A₂, A₃, ... are nonempty closed convex subsets of X with A = τM — lim An , then A° = τM — lim A°/n ; (2) τM is a Hausdorff topology on the nonempty closed convex subsets of X ; (3) the arg min multifunction ∫ ⇉ {x ∈ X : ∫(x) = infx ∫} on the proper lower semicontinuous convex functions on X , equipped with τM , has closed graph.

Item Type: Article
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 18 Feb 2015 15:02
Last Modified: 18 Feb 2015 15:02

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