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Mosco convergence and weak topologies for convex sets and functions

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

Gerald Beer
Gerald Beer
Affiliation:
Professor G. Beer, Department of Mathematics, California State University, Los Angeles, Los Angeles, California 90032, U.S.A.
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Abstract

Let X be a reflexive Banach space. This article presents a number of new characterizations of the topology of Mosco convergence TM for convex sets and functions in terms of natural geometric operators and functional. In addition, necessary and sufficient conditions are given for TM to agree with the weak topology generated by {d(x, C): x є X}, where each distance functional is viewed as a function of the set argument.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Mathematika , Volume 38 , Issue 1 , June 1991 , pp. 89 - 104
Copyright
Copyright © University College London 1991

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