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Complemented Copies of l 1 in Spaces of Vector Measures and Applications
Author(s) -
Randrianantoanircisse
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19992020109
Subject(s) - mathematics , hausdorff space , banach space , locally compact space , characterization (materials science) , norm (philosophy) , bounded variation , space (punctuation) , pure mathematics , dual space , continuous functions on a compact hausdorff space , bounded function , vector space , discrete mathematics , dual (grammatical number) , mathematical analysis , linguistics , philosophy , materials science , political science , law , nanotechnology , art , literature
Let X be a dual Banach space and Ω 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 ∑ of Borel subsets of Ω 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 Pełczyński's property ( V *) then so does the space of X‐ valued countably additive measures with the usual variation norm.