Asplund spaces, Stegall variational principle and the RNP

Marc Lassonde (1)

1 LAMIA - Laboratoire de Mathématiques Informatique et Applications

Given a pair of Banach spaces X and Y such that one is the dual of the other, we study the relationships between generic Fréchet differentiability of convex continuous functions on Y (Asplund property), generic existence of linear perturbations for lower semicontinuous functions on X to have a strong minimum (Stegall variational principle), and dentability of bounded subsets of X (Radon-Nikodým Property).

Domaines: Optimisation et contrôle [math.OC]; Analyse fonctionnelle [math.FA]

Marc Lassonde. Asplund spaces, Stegall variational principle and the RNP. Set-Valued Analysis, 2009, 17 (2), pp.183-193. ⟨hal-00694604⟩