Strong barrelledness properties in B(Σ, X)

Publisher: Cambridge University Press

E-ISSN: 1755-1633|52|2|207-214

ISSN: 0004-9727

Source: Bulletin of the Australian Mathematical Society, Vol.52, Iss.2, 1995-10, pp. : 207-214

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Abstract

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.