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Strong barrelledness properties in B(Σ, X)

Published online by Cambridge University Press:  17 April 2009

J.C. Ferrando  and
L. M. Sánchez Ruiz
J.C. Ferrando
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain, e-mail: [email protected]@upvnet.upv.es
L. M. Sánchez Ruiz
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain, e-mail: [email protected]@upvnet.upv.es
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Abstract

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In this paper we show that given a σ-algebra Σ of subsets of a set Ω and a normed space X, then the normed space B(Σ, X), endowed with the usual supremum-norm, of the X-valued functions defined on Ω that are the uniform limit of a sequence of σ-simple X-valued functions on Ω is barrelled of class s if and only if X is barrelled of class s. This extends in the normed case the well known result obtained by Mendoza (1982) for barrelled spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 207 - 214
Copyright
Copyright © Australian Mathematical Society 1995

References

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