On a sufficient condition for proximity

Author:
Ka Sing Lau

Journal:
Trans. Amer. Math. Soc. **251** (1979), 343-356

MSC:
Primary 46B99; Secondary 41A65, 47D15

DOI:
https://doi.org/10.1090/S0002-9947-1979-0531983-0

MathSciNet review:
531983

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Abstract | References | Similar Articles | Additional Information

Abstract: A closed subspace *M* in a Banach space *X* is called *U*-proximinal if it satisfies: , for some positive valued function , , and as , where *S* is the closed unit ball of *X*. One of the important properties of this class of subspaces is that the metric projections are continuous. We show that many interesting subspaces are *U*-proximinal, for example, the subspaces with the 2-ball property (semi *M*-ideals) and certain subspaces of compact operators in the spaces of bounded linear operators.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0531983-0

Keywords:
Compact operators,
measurable functions,
*M*-ideals,
proximity,
uniformly convex

Article copyright:
© Copyright 1979
American Mathematical Society