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Comparable characterisations of two classes of Banach spaces by subdifferentials

Published online by Cambridge University Press:  17 April 2009

J.R. Giles
J.R. Giles
Affiliation:
Department of Mathematics, The University of Newcastle, New South Wales 2308, Australia
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Abstract

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We characterise Banach spaces not containing ℓ1 and Banach spaces which are Asplund spaces by continuity properties of the subdifferential mappings of their equivalent norms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 155 - 158
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Deville, R., Godefroy, G. and Zizler, V., Smoothness and renormings in Banach spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics 64 (Longman Scientific and Technical, Harlow, 1993).Google Scholar
[2]Giles, J.R., ‘Comparable differentiability characterisations of two classes of Banach spaces’, Bull. Austral. Math. Soc. 56 (1997), 263–272.CrossRefGoogle Scholar
[3]Giles, J.R., Gregory, D.A. and Sims, B., ‘Geometrical implications of upper semi-continuity of the duality mapping on a Banach space’, Pacific J. Math. 79 (1978), 99–109.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]Phelps, R.R., Convex functions, monotone operators and differentiability (2nd ed.), Lecture Notes in Math. 1364 (Springer-Verlag, Berlin, Heidelberg, New York, 1993).Google Scholar