Vol. 99, No. 1, 1982

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On the proximinality of Stone-Weierstrass subspaces

Jaroslav Mach

Vol. 99 (1982), No. 1, 97–104
Abstract

Let S be a compact Hausdorff space, X a Banach space, C(S,X) the Banach space of all continuous X-valued functions on S equipped with the supremum norm. In this paper a necessary and sufficient condition on X for every Stone-Weierstrass subspace of C(S,X) to be proximinal is established. Furthermore, it is shown that every such subspace is proximinal if X is a dual locally uniformly convex space.

Mathematical Subject Classification 2000
Primary: 41A50
Secondary: 41A45, 46E25
Milestones
Received: 21 December 1979
Revised: 22 January 1981
Published: 1 March 1982
Authors
Jaroslav Mach