Banach spaces in which every compact lies inside the range of a vector measure

Authors:
C. Piñeiro and L. Rodríguez-Piazza

Journal:
Proc. Amer. Math. Soc. **114** (1992), 505-517

MSC:
Primary 46B20; Secondary 46G10

MathSciNet review:
1086342

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Abstract: We prove that the compact subsets of a Banach space lie inside ranges of -valued measures if and only if can be embedded in an space. In these spaces we prove that every compact is, in fact, a subset of a compact range. We also prove that if every compact of is a subset of the range of an -valued measure of bounded variation, then is finite dimensional. Thus we answer a question by R. Anantharaman and J. Diestel.

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DOI:
https://doi.org/10.1090/S0002-9939-1992-1086342-3

Keywords:
Vector measures,
range,
Banach spaces,
compact sets,
subspaces of

Article copyright:
© Copyright 1992
American Mathematical Society