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Separable measures and the Dunford-Pettis property

Published online by Cambridge University Press:  17 April 2009

José Aguayo  and
José Sánchez
José Aguayo
Affiliation:
Departamento de Matemática, Universidad de Concepción, Casilla 3-C. Concepción, Chile
José Sánchez
Affiliation:
Departamento de Matemática, Universidad de Concepción, Casilla 3-C. Concepción, Chile
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Abstract

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Let X be a complete regular space. We denote by Cb(X) the Banach space of all real-valued bounded continuous functions on X endowed with the supremumnorm.

In this paper we give a characterisation of weakly compact operators defined from Cb(X) into a Banach space E which are β∞-continuous, where β∞ is a locally convex topology on Cb(X) introduced by Wheeler. We also prove that (Cb(X), β∞) has the strict Dunford-Pettis property and, if X is a σ-compact space, (Cb(X), β∞), has the Dunford-Pettis property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 423 - 428
Copyright
Copyright © Australian Mathematical Society 1991

References

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