Banach spaces in which every compact lies inside the range of a vector measure
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- by C. Piñeiro and L. Rodríguez-Piazza PDF
- Proc. Amer. Math. Soc. 114 (1992), 505-517 Request permission
Abstract:
We prove that the compact subsets of a Banach space $X$ lie inside ranges of $X$-valued measures if and only if ${X^*}$ can be embedded in an ${L^1}$ 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 $X$ is a subset of the range of an $X$-valued measure of bounded variation, then $X$ is finite dimensional. Thus we answer a question by R. Anantharaman and J. Diestel.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 114 (1992), 505-517
- MSC: Primary 46B20; Secondary 46G10
- DOI: https://doi.org/10.1090/S0002-9939-1992-1086342-3
- MathSciNet review: 1086342