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Title: Criteria for weak compactness of vector-valued integration maps (English)
Author: Okada, S.
Author: Ricker, W. J.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 35
Issue: 3
Year: 1994
Pages: 485-495
Category: math
Summary: Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration maps of a class of measures taking their values in $\ell^1$, equipped with various weak topologies. (English)
Keyword: weakly compact integration map
Keyword: factorization of a vector measure
MSC: 28B05
MSC: 46A05
MSC: 46E30
MSC: 46G10
MSC: 47B07
MSC: 47B38
idZBL: Zbl 0805.46040
idMR: MR1307275
Date available: 2009-01-08T18:12:41Z
Last updated: 2012-04-30
Stable URL:
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