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Chebyshev centres and centrable sets

Author: T. S. S. R. K. Rao
Journal: Proc. Amer. Math. Soc. 130 (2002), 2593-2598
MSC (2000): Primary 41A65, 46B20
Published electronically: April 17, 2002
MathSciNet review: 1900866
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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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  • [BR] P. Bandyopadhyay and T. S. S. R. K. Rao, Central subspaces of Banach spaces, J. Approx. Theory, 103 (2000) 206-222. MR 2001b:46022
  • [C] F. Cabello Sanchez, Diameter preserving linear maps and isometries, Arch. Math., 73(1999) 373-379. MR 2000j:46047
  • [DU] J. Diestel and J. J. Uhl, Vector measures, AMS Surveys No 15, Providence, RI, 1977. MR 56:12216
  • [E] R. Espínola, A. Wisnicki and J. Wosko, A geometrical characterization of the $C(K) $ and $C_0(K)$ spaces, J. Approx. Theory, 105 (2000) 87-101. MR 2001g:46026
  • [FS] J. J. Font and M. Sanchis, A characterization of locally compact spaces with homeomorphic one point compactification, Top. Appl., to appear.
  • [H] R. B. Holmes, A course on optimization and best approximation, LNM No 257, Springer-Verlag, Berlin, 1972. MR 54:8381
  • [HS] Z. Hu and M. Smith, On the extremal structure of the unit ball of the space $C(K,X)^\ast$, in: Proc. Conf. on Function Spaces (SIUE), Lecture Notes in Pure and Appl. Math. No 172, Marcel Dekker, 1995, 205-223. MR 96k:46062
  • [Hu] O. Hustad, A note on complex ${\cal P}_1$-spaces, Israel J. Math., 16 (1973) 117-119. MR 48:9351
  • [L] H. E. Lacey, Isometric theory of classical Banach spaces, Grundlehren Math. Wiss., Band 208, Springer-Verlag, Berlin, 1973. MR 58:12308
  • [LLT] B. L. Lin, P. K. Lin and S. L. Troyanski, Characterizations of denting points, Proc. Amer. Math. Soc., 102 (1988) 526-528. MR 89e:46016
  • [RR] T. S. S. R. K. Rao and A. K. Roy, Diameter-preserving linear bijections of function spaces, J. Austral. Math. Soc., 70 (2001) 323-335. MR 2002b:46039

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Additional Information

T. S. S. R. K. Rao
Affiliation: Indian Statistical Institute, R. V. College Post, Bangalore-560059, India

Keywords: Chebyshev centre, centrable set, diameter norm
Received by editor(s): February 12, 2001
Published electronically: April 17, 2002
Dedicated: Dedicated to the memory of my father
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2002 American Mathematical Society

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