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On the lower semicontinuity of the set-valued metric projection

โœ Scribed by Bruno Brosowski; Rudolf Wegmann

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
700 KB
Volume
8
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