Properties of Dunford-Pettis type in topological groups
by
E. Martín-Peinador
University Complutense at Madrid, Spain
Coauthors: V. Tarieladze (Georgian Academy of Sciences, Georgia)

The property of Dunford-Pettis for a locally convex space was introduced by Grothendieck in 1953. It has been intensively studied, with especial emphasis in the framework of Banach space theory.

In this paper we define the Bohr sequential continuity property (BSCP), which could be the analogous notion to Dunford-Pettis property in the context of topological Abelian groups. We have picked this name because the Bohr topology of the group and of the dual group play an important role in the definition. We prove that a separable Pontryagin reflexive group has BSCP if and only if it has the Schur property. Section § 3 deals with the relationship between those two properties.

For a locally convex space, considered in its additive structure, we see that BSCP is stronger than the Dunford-Pettis property ; more concretely, for a separable Frechet space BSCP is equivalent to Schur property.

Date received: March 28, 2001

Copyright © 2001 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 # cafw-73.