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Complemented Copies of l1 in Spaces of Vector Measures and Applications

✍ Scribed by Narcisse Randrianantoanina

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
771 KB
Volume
202
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let X be a dual Banach space and Ξ© be a compact Hausdorff space. We give a characterization af those sequences in the space of all regular X‐ valued countably additive measures with bounded variation, defined on the σ‐ field βˆ‘ of Borel subsets of Ξ© which generate complemented copies of l~1~, in terms of weak*‐densities. As an application, we prove that if a dual Banach space X has PeΕ‚czyΕ„ski's property (V*) then so does the space of X‐ valued countably additive measures with the usual variation norm.

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