Three space properties and asymptotic properties of Banach spaces.

Philip H. Brooker (1) , Gilles Lancien (1)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

Domaines: Analyse fonctionnelle [math.FA]

Philip H. Brooker, Gilles Lancien. Three space properties and asymptotic properties of Banach spaces.. Journal of Mathematical Analysis and Applications, 2013, 398 (2), pp.867-871. ⟨hal-00825051⟩