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Chebyshev centres and centrable sets

Author(s): T. S. S. R. K. Rao
Journal: Proc. Amer. Math. Soc. 130 (2002), 2593-2598.
MSC (2000): Primary 41A65, 46B20
Posted: April 17, 2002
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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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Additional Information:

T. S. S. R. K. Rao
Affiliation: Indian Statistical Institute, R. V. College Post, Bangalore-560059, India
Email: tss@isibang.ac.in

DOI: 10.1090/S0002-9939-02-06624-8
PII: S 0002-9939(02)06624-8
Keywords: Chebyshev centre, centrable set, diameter norm
Received by editor(s): February 12, 2001
Posted: April 17, 2002
Dedicated: Dedicated to the memory of my father
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2002, American Mathematical Society

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