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

DOI:
https://doi.org/10.1090/S0002-9939-96-03541-1

MathSciNet review:
1346973

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Abstract: We characterize those Banach spaces , in which every -valued measure with relatively compact range admits product with any vector measure and with respect to any bilinear map, as those such that . We also show that this condition is equivalent to the condition that every sequence in 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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Additional Information

**Juan Carlos García-Vázquez**

Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain

Email:
garcia@cica.es

DOI:
https://doi.org/10.1090/S0002-9939-96-03541-1

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