Smoothness, asymptotic smoothness and the Blum-Hanson property

Etienne Matheron (1) , Armel Primot (1) , Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens

We isolate various su cient conditions for a Banach space X to have the so-called Blum-Hanson property. In particular, we show that X has the Blum-Hanson property if either the modulus of asymptotic smoothness of X has an extremal behaviour at in nity, or if X is uniformly G^ateaux smooth and embeds isometrically into a Banach space with a 1-unconditional nite-dimensional decomposition.

Domaines: Analyse fonctionnelle [math.FA]

Etienne Matheron, Armel Primot, Pascal Lefèvre. Smoothness, asymptotic smoothness and the Blum-Hanson property. 2013. ⟨hal-00859177⟩