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Strong barrelledness properties in B(Σ, X)
Published online by Cambridge University Press: 17 April 2009
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.
- 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
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