A dual characterisation of the Radon-Nikodym property

Mohammed Bachir 1 Aris Daniilidis 2
1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
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 $X$.
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Submitted on : Friday, August 7, 2015 - 12:28:32 AM
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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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