Modulus of Strong Proximinality and Continuity of Metric Projection |
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Authors: | S. Dutta P. Shunmugaraj |
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Affiliation: | 1.Department of Mathematics and Statistics,Indian Institute of Technology Kanpur,Kanpur,India |
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Abstract: | In this paper we initiate a quantitative study of strong proximinality. We define a quantity ϵ(x, 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 ϵ(x, t) is continuous at x whenever t > 0. The best possible estimate of ϵ(x, t) characterizes spaces with 1 frac121 frac{1}{2} ball property. Estimates of ϵ(x, t) are obtained for subspaces of uniformly convex spaces and of strongly proximinal subspaces of finite codimension in C(K). |
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