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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Reflexivity and norm attaining functionals
by
Maria D. Acosta
Universidad de Granada
Coauthors: Julio Becerra Guerrero (Universidad de Granada), Manuel Ruiz Galan (Universidad de Granada)

The most famous result relating the set of norm attaining functionals of a Banach space and reflexivity is James' Theorem: a Banach space is reflexive if all the (bounded and linear) functionals on it attain the norm. There are several statements along the same line by assuming a weaker condition on the set of norm attaining functionals and some additional assumption on the Banach space. Amongst them, there are results by Bourgain, Stegall, Petunin and Plichko, Kenderov, Moors and Sciffer and Jimenez Sevilla and Moreno. For instance, if the set of norm attaining functionals has non empty interior and the space satisfies some isometric condition (Hahn-Banach smoothness or the Mazur intersection property), then the space is reflexive. We prove that a Banach space is reflexive as soon as it does not contain l1 and the unit ball of the dual space is the w * -closure of some points in the ''uniform" interior of the set of norm attaining functionals. Also, we exhibit examples which show that the result is sharp.

(T)

Date received: April 11, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caey-05.