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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Tensor products of vector measures and
sequences in the range of a vector measure

Author: Juan Carlos García-Vázquez
Journal: Proc. Amer. Math. Soc. 124 (1996), 3459-3467
MSC (1991): Primary 46B28, 46G10
MathSciNet review: 1346973
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Abstract: We characterize those Banach spaces $X$, in which every $X$-valued measure with relatively compact range admits product with any vector measure and with respect to any bilinear map, as those $X$ such that $\Pi _{1} (X,\ell _{1}) = {\mathcal {L}} (X,\ell _{1})$. We also show that this condition is equivalent to the condition that every sequence in $X$ that lies inside the range of a measure with relatively compact range, actually lies inside the range of a measure of bounded variation.

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Juan Carlos García-Vázquez
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain

Received by editor(s): May 31, 1995
Additional Notes: Research supported by DGICYT grant PB93-0926. This work is from the author’s Doctoral Thesis which is being prepared at the Universidad de Sevilla, under the supervision of Prof. Francisco J. Freniche.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society