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On the weak*-Radon Nikodym property

Published online by Cambridge University Press:  17 April 2009

Elias Saab
Elias Saab
Affiliation:
Department of Mathematics, University of Missouri, Columbia, MO 65211
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Abstract

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We say that a certain property in a Banach space E is stable by subspaces if every closed subspace of E enjoys the same property. It is well known that the Radon-Nikodym property is stable by subspaces while the Weak Radon-Nikodym property is not. In his recent memoir, Talagrand investigated the stability of the Weak*Radon-Nikodym property which is a generalization of the Weak Radon-Nikodym property and showed that under Axiom L, the Weak*Radon-Nikodym property is stable by subspaces. It is still an open problem whether or not this result holds without this extra set theoretical hypothesis. In this paper we show that in a dual Banach space, the Weak*Radon-Nikodym property is stable by subspaces without assuming Axiom L. Other related results are discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 3 , June 1988 , pp. 323 - 332
Copyright
Copyright © Australian Mathematical Society 1988

References

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