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A locally uniformly convex renorming for certain ℒ(K)

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

R. G. Haydon  and
C. A. Rogers
R. G. Haydon
Affiliation:
Brasenose College, Oxford, OX1 4AJ
C. A. Rogers
Affiliation:
Department of Statistical Science, University College London, Gower Street, London, WC1E 6BT
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Abstract

If a scattered compact space K is such that its ω1-th derived set K(ω1) is empty then the Banach space ℒ(K) admits an equivalent locally uniformly convex norm.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Mathematika , Volume 37 , Issue 1 , June 1990 , pp. 1 - 8
Copyright
Copyright © University College London 1990

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References

1.Day, M. M.. Normed linear spaces (3rd ed.) (Springer-Verlag, Berlin-Heidelberg-New York, 1973).CrossRefGoogle Scholar
2.Deville, R.. Problemes de renormages. J. Fund. Anal., 68 (1986), 117–129.Google Scholar
3.Deville, R.. Convergence ponctuelle et uniforme sur un espace compact. Bull. Acad. Polon. Sci. (to appear).Google Scholar
4.Deville, R. and Godefroy, G.. Some applications of projective resolutions of unity (preprint).Google Scholar
5.Godefroy, G., Troyanski, S. L., Whitfield, J. and Zizler, V.. Locally uniformly rotund renormings and injections into c o(Γ). Canad. Math. Bull, 27 (1984), 494–500.CrossRefGoogle Scholar
6.Godefroy, G., Troyanski, S. L., Whitfield, J. and Zizler, V.. Three-space problem for locally uniformly rotund renormings of Banach spaces. Proc. Amer. Math. Soc, 94 (1985), 647–652.Google Scholar
7.Haydon, R. G.. A counterexample to several questions about scattered compact spaces (to appear), Bull. London Math. Soc.Google Scholar
8.Jayne, J. E., Namioka, I. and Rogers, C. A., σ-fragmentable Banach spaces (preprint).Google Scholar
9.Namioka, I. and Phelps, R. R.. Banach spaces which are Asplund spaces. Duke Math. J., 42 (1875), 735–750.Google Scholar
10.Semadeni, Z.. Banach spaces of continuous functions (P.W.N., Warszawa, 1971).Google Scholar