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Journal Articles Bulletin of the Australian Mathematical Society Year : 2000

A dual characterisation of the Radon-Nikodym property

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Mohammed Bachir
• Function : Author
• PersonId : 960537
Aris Daniilidis
• Function : Author
• PersonId : 843792

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 $X$.

Dates and versions

hal-01183280 , version 1 (07-08-2015)

Identifiers

• HAL Id : hal-01183280 , version 1

Cite

Mohammed Bachir, Aris Daniilidis. A dual characterisation of the Radon-Nikodym property. Bulletin of the Australian Mathematical Society, 2000, 62, pp.379-387. ⟨hal-01183280⟩

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