Simultaneously proximinal subspaces

Authors

T. S.S.R.K. Rao, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Journal of Applied Analysis

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.

First Page

115

Last Page

120

DOI

10.1515/jaa-2016-0012

Publication Date

12-1-2016

Recommended Citation

Rao, T. S.S.R.K., "Simultaneously proximinal subspaces" (2016). Journal Articles. 4445.
https://digitalcommons.isical.ac.in/journal-articles/4445