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Weakly compact operators and the strict topologies

Published online by Cambridge University Press:  17 April 2009

José Aguayo  and
José Sánchez
José Aguayo
Affiliation:
Departmento de Matematica Facultad de Ciencias, Universidad de Concepcion, Casilla 2017, Concepcion, Chile
José Sánchez
Affiliation:
Departmento de Matematica Facultad de Ciencias, Universidad de Concepcion, Casilla 2017, Concepcion, Chile
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Abstract

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

In this paper we prove some characterisations of weakly compact operators defined from Cb(X) into a Banach space E which are continuous with respect to fit, βt, βr and βσ introduced by Sentilles.

We also prove that (Cb,(X), βi), i = t, τσ , has the Dunford-Pettis property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 3 , June 1989 , pp. 353 - 359
Copyright
Copyright © Australian Mathematical Society 1989

References

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