Dual spaces generated by the interior of the set of norm attaining functionals

• Autorzy: Maria D. Acosta , Julio Becerra Guerrero , Manuel Ruiz Galán
• Języki publikacji: EN

Abstrakty

EN

We characterize some isomorphic properties of Banach spaces in terms of the set of norm attaining functionals. The main result states that a Banach space is reflexive as soon as it does not contain ℓ₁ and the dual unit ball is the w*-closure of the convex hull of elements contained in the "uniform" interior of the set of norm attaining functionals. By assuming a very weak isometric condition (lack of roughness) instead of not containing ℓ₁, we also obtain a similar result. As a consequence of the first result, a convex-transitive Banach space not containing ℓ₁ and such that the set of norm attaining functionals has nonempty interior is in fact superreflexive.

Kategorie tematyczne

• 46B10: Duality and reflexivity
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 2
• Strony: 175-183

Daty

wydano

2002

Twórcy

autor

Maria D. Acosta

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

autor

Julio Becerra Guerrero

• Departamento de Matemática Aplicada, E.U. Arquitectura Técnica, Universidad de Granada, 18071 Granada, Spain

autor

Manuel Ruiz Galán

• Departamento de Matemática Aplicada, E.U. Arquitectura Técnica, Universidad de Granada, 18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm149-2-6