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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sequences in the range of a vector measure with bounded variation


Author: Cándido Piñeiro
Journal: Proc. Amer. Math. Soc. 123 (1995), 3329-3334
MSC: Primary 46B20; Secondary 28B05, 46G10
MathSciNet review: 1291790
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Abstract: Let X be a Banach space. We consider sequences $ ({x_n})$ in X lying in the range of a measure valued in a superspace of X and having bounded variation. Among other results, we prove that G.T. spaces are the only Banach spaces in which those sequences are actually in the range of an $ {X^{ \ast\ast }}$-valued measure of bounded variation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1291790-5
PII: S 0002-9939(1995)1291790-5
Article copyright: © Copyright 1995 American Mathematical Society