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A dual characterisation of the Radon-Nikodym property
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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