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A dual characterisation of the Radon-Nikodym property

Published online by Cambridge University Press:  17 April 2009

M. Bachir  and
A. Daniilidis
M. Bachir
Affiliation:
Laboratoire de Mathématiques Pures, Université Bordeaux I, 351 cours de la Libération, 33405 Talence Cedex, France e-mail: bachir@math.u-bordeaux.fr
A. Daniilidis
Affiliation:
Laboratoire de Mathématiques Appliquées, CNRS ERS 2055, Université de Pau et des Pays de l'Adour, Avenue de l'Université, 64000 Pau, France e-mail: aris.daniilidis@univ-pau.fr
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Abstract

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We prove that a Banach space X has the Radon-Nikodym property if, and only if, every weak*-lower semicontinuous convex continuous function f of X* is Gâteaux differentiable at some point of its domain with derivative in the predual space x.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 3 , December 2000 , pp. 379 - 387
Copyright
Copyright © Australian Mathematical Society 2000

References

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