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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 $X$.
https://hal-paris1.archives-ouvertes.fr/hal-01183280 Contributor : Mohammed BachirConnect in order to contact the contributor Submitted on : Friday, August 7, 2015 - 12:28:32 AM Last modification on : Friday, May 6, 2022 - 4:50:07 PM
Mohammed Bachir, Aris Daniilidis. A dual characterisation of the Radon-Nikodym property. Bulletin of the Australian Mathematical Society, John Loxton University of Western Sydney|Australia 2000, 62, pp.379-387. ⟨hal-01183280⟩