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On the Norm of the Metric Projections

✍ Scribed by Fernando Mazzone

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 87 KB
Volume: 97
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1996.3271

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✦ Synopsis

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 |2Â p&1| , for every subspace M of L p . We also show that ?(X )=?(X*).

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