Modulus of Strong Proximinality and Continuity of

Authors: S Dutta P Shunmugaraj

Publish Date: 2010/07/24

Volume: 19, Issue: 2, Pages: 271-281

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Abstract

In this paper we initiate a quantitative study of strong proximinality We define a quantity ϵx t which we call as modulus of strong proximinality and show that the metric projection onto a strongly proximinal subspace Y of a Banach space X is continuous at x if and only if ϵx t is continuous at x whenever t  0 The best possible estimate of ϵx t characterizes spaces with 1 frac12 ball property Estimates of ϵx t are obtained for subspaces of uniformly convex spaces and of strongly proximinal subspaces of finite codimension in CK

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