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Comparable differentiability characterisations of two classes of Banach spaces

Published online by Cambridge University Press:  17 April 2009

J.R. Giles
J.R. Giles
Affiliation:
Department of MathematicsThe University of NewcastleNew South Wales 2308Australia
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Abstract

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We characterise Banach spaces not containing l1 by a differentiability property of each equivalent norm and show that a slightly stronger differentiability property characterises Asplund spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 263 - 272
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Pitman monographs 64 (Longman, Essex, New York, 1993).Google Scholar
[2]Diestel, J. and Uhl, J.J., Vector measures, Math. Surveys 15 (American Mathematical Society, Providence, R.I., 1977).CrossRefGoogle Scholar
[3]Godefroy, G., ‘Metric characterisation of first Baire class linear forms and octahedral norms’, Studia Math. 95 (1989), 1–15.CrossRefGoogle Scholar
[4]Huff, R.E. and Morris, P.D., ‘Dual spaces with the Krein–Milman property have the Radon–Nikodym property’, Proc. Amer. Math. Soc. 49 (1975), 104–108.Google Scholar
[5]Kuo, T–H, ‘On conjugate Banach spaces with the Radon–Nikodym Property’, Pacific J. Math. 59 (1975), 497–503.CrossRefGoogle Scholar
[6]Phelps, R.R., Convex functions, monotone operators and differentiability, Lecture Notes in Math. 1364, (2nd ed.) (Springer-Verlag, Berlin, Heidelberg, New York, 1993).Google Scholar
[7]Saab, E. and Saab, P., ‘A dual geometric characterization of Banach spaces not containing l 1’, Pacific J. Math. 105 (1983), 415–425.CrossRefGoogle Scholar
[8]van Dulst, D., Characterizations of Banach spaces not containing l 1 (Centrum voor Wiskunde en Informatica Tract 59, Amsterdam, 1989).Google Scholar