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A property of Dunford-Pettis type in topological groups

Martín Peinador, Elena and Tarieladze, Vaja (2003) A property of Dunford-Pettis type in topological groups. Proceedings of the American Mathematical Society, 132 (6). pp. 1827-1837. ISSN 1088-6826

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Abstract

The property of Dunford-Pettis for a locally convex space was introduced by Grothendieck in 1953. Since then 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) for a topological Abelian group. This notion could be the analogue to the Dunford-Pettis property in the context of groups. We have picked this name because the Bohr topology of the group and of the dual group plays an important role in the definition. We relate the BSCP with the Schur property, which also admits a natural formulation for Abelian topological groups, and we prove that they are equivalent within the class of separable metrizable locally quasi-convex groups.
For Banach spaces (or for metrizable locally convex spaces), considered in their additive structure, we show that the BSCP lies between the Schur and the Dunford-Pettis properties.


Item Type:Article
Uncontrolled Keywords:Dunford-Pettis property; Schur property; Bohr topology; Dual group; Pontryagin reflexive; Locally convex space
Subjects:Sciences > Mathematics > Topology
ID Code:12706
Deposited On:11 May 2011 09:38
Last Modified:06 Feb 2014 09:30

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