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A dual characterisation of the existence of small combinations of slices

Published online by Cambridge University Press:  17 April 2009

Robert Deville
Robert Deville
Affiliation:
Equipe d'Analyse fonctionelle, Université Paris VIFRANCE.
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Abstract

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We characterise, by a property of roughness, the norms of a Banach space X such that the dual unit ball has no small combination of ω*-slices. Among separable Banach spaces, the existence of an equivalent norm for this new property of roughness characterises spaces which contain an isomorphic copy of ℓ1(N).

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 113 - 120
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Bourgain, J., ‘La propriete de Radon Nikodym’, Publications de I'université Pierre et Marie Curie 36 (1979).Google Scholar
[2]Goussoub, N., Godefroy, G., Maurey, B. and Schachermayer, W., ‘Some topological and geometrical structures in Banach spaces’, Mem. Amer. Math. Soc. (to appear).Google Scholar
[3]Godefroy, G. and Maurey, B., ‘Normes lisses et normes anguleuses sur les espaces de Banach separables’ (to appear).Google Scholar
[4]Godini, G., ‘Rough and strongly rough norms on Banach spaces’, Proc. Amer. Math. Soc. 87 (1983), 239–245.CrossRefGoogle Scholar
[5]John, K. and Zizler, V., ‘On rough norms on Banach spaces’, Comment. Math. Univ. Carotin. 19 (1978), 335–349.Google Scholar
[6]Leach, E.B. and Whitfield, J.H.M, ‘Differentiable functions and rough norms on Banach spaces’, Proc. Amer. Math. Soc. 33 (1972), 120–126.CrossRefGoogle Scholar
[7]Rosenthal, H.P., ‘On the structure of non-dentable closed bounded convex sets’ (to appear).Google Scholar
[8]Sullivan, F., ‘Dentability, smoothability and stronger properties in Banach spaces’, Indiana Univ. Math. J. 26 (1977), 545–553.CrossRefGoogle Scholar
[9]Whitfield, J. and Zizler, V., ‘A survey of rough norms with applications’, Contemp. Math. 54 (1986).CrossRefGoogle Scholar
[10]Van Dulst, D., ‘Reflexive and superreflexive Banach spaces’, Mathematical Centre Tracts 102, Amsterdam 1978.Google Scholar