A dual characterisation of the Radon-Nikodym property

Mohammed Bachir (1) , Aris Daniilidis (2)

1 Equations d'evolution
2 UAB - Departament de Matemàtiques [Barcelona]

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 $X$.

Domains: Functional Analysis [math.FA]

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⟩