On -summable sequences in the range

of a vector measure

Author:
Cándido Piñeiro

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2073-2082

MSC (1991):
Primary 46G10; Secondary 47B10

DOI:
https://doi.org/10.1090/S0002-9939-97-03817-3

MathSciNet review:
1377003

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Abstract: Let . Among other results, we prove that a Banach space has the property that every sequence lies inside the range of an -valued measure if and only if, for all sequences in satisfying that the operator is 1-summing, the operator is nuclear, being the conjugate number for . We also prove that, if is an infinite-dimensional -space for , then can't have the above property for any .

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Additional Information

**Cándido Piñeiro**

Email:
candido@colon.uhu.es

DOI:
https://doi.org/10.1090/S0002-9939-97-03817-3

Received by editor(s):
November 30, 1995

Received by editor(s) in revised form:
January 31, 1996

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society