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The continuity of metric projections as functions of the data

โœ Scribed by James W Daniel

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
464 KB
Volume
12
Category
Article
ISSN
0021-9045

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Let X be a Banach space. Given M a subspace of X we denote with P M the metric projection onto M. We define ?(X ) :=sup [&P M &: M a proximinal subspace of X]. In this paper we give a bound for ?(X ). In particular, when X=L p , we obtain the inequality &P M & 2 |2ร‚ p&1| , for every subspace M of L

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In 1979, Bjornestal obtained a local estimate for a modulus of uniform continuity of the metric projection operator on a closed subspace in a uniformly convex and uniformly smooth Banach space B. In the present paper we give the global version of this result for the projection operator on an arbitra