- Title
- Mosco convergence and reflexivity
- Creator
- Beer, Gerald; Borwein, Jonathan M.
- Relation
- Proceedings of the American Mathematical Society Vol. 109, Issue 2, p. 427-436
- Publisher Link
- http://dx.doi.org/10.1090/S0002-9939-1990-1012924-9
- Publisher
- American Mathematical Society
- Resource Type
- journal article
- Date
- 1990
- Description
- 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.
- Subject
- Mosco convergence; polar convex set; conjugate convex function; arg min multifunction; reflexivity
- Identifier
- http://hdl.handle.net/1959.13/940522
- Identifier
- uon:13028
- Identifier
- ISSN:0002-9939
- Rights
- First published in Proceedings of the American Mathematical Society in Vol. 109, No. 2, pp. 427-436, 1990, published by the American Mathematical Society.
- Language
- eng
- Full Text
- Reviewed
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