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Simultaneously proximinal subspaces

  • T. S. S. R. K. Rao EMAIL logo
Published/Copyright: November 11, 2016

Abstract

In this paper we study closed subspaces of Banach spaces that admit relative Chebyshev centers for all bounded subsets of the space. We exhibit new classes of spaces which have this property and study stability results similar to the ones studied in the literature in the context of proximinal subspaces and Chebyshev centers. For the space C(K) of continuous functions on a compact set K, we show that a closed subspace of finite codimension has relative Chebyshev centers for all bounded sets in C(K) if and only if it is a strongly proximinal subspace.

MSC 2010: 41A50; 46B20

Acknowledgements

Thanks are due to the referees for pointing out several corrections and for their comments. The author was a Fulbright-Nehru Academic and Professional Excellence Fellow at the Department of Mathematical Sciences, University of Memphis, during 2015–16.

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Received: 2015-4-17
Revised: 2016-2-4
Accepted: 2016-4-14
Published Online: 2016-11-11
Published in Print: 2016-12-1

© 2016 by De Gruyter

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