A new proof of James' sup theorem

Marianne Morillon (1)

1 ERMIT - Equipe Réunionnaise de Mathématiques et Informatique Théorique

We provide a new proof of James' sup theorem for (non necessarily separable) Banach spaces. One of the ingredients is the following generalization of a theorem of Hagler and Johnson (1977) : "If a normed space $E$ does not contain any asymptotically isometric copy of $\ell^1(\IN)$, then every bounded sequence of $E'$ has a normalized block sequence pointwise converging to $0$".

Mots clés: James' sup theorem; block sequences; reflexive Banach spaces; Axiom of Choice

Domaines: Analyse fonctionnelle [math.FA]

Marianne Morillon. A new proof of James' sup theorem. 2005. ⟨hal-00004892⟩