Chebyshev centres and centrable sets

Rao, T.

doi:10.1090/S0002-9939-02-06624-8

Chebyshev centres and centrable sets
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by T. S. S. R. K. Rao PDF

Proc. Amer. Math. Soc. 130 (2002), 2593-2598 Request permission

Abstract:

In this paper we characterize real Banach spaces whose duals are isometric to $L^1(\mu )$ spaces (the so-called $L^1$-predual spaces) as those spaces in which every finite set is centrable. For a locally compact, non-compact set $X$ and for an $L^1$-predual $E$, we give a complete description of the extreme points and denting points of the dual unit ball of $C_0(X,E)$, equipped with the diameter norm.

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