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Proceedings of the American Mathematical Society

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

 

 

$ L\sp{1}\sb{x}$ is weakly compactly generated if $ X$ is


Author: J. Diestel
Journal: Proc. Amer. Math. Soc. 48 (1975), 508-510
MSC: Primary 46E40; Secondary 46B05
MathSciNet review: 0367651
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Abstract: Though good criteria for weak compactness in the space of Bochner-integrable functions are not yet known, one can show that $ {L_1}(\mu ;X)$ is a weakly compactly generated Banach space whenever $ \mu $ is finite and $ X$ is a weakly compactly generated Banach space. The proof depends upon a recent factorization scheme due to W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0367651-X
Keywords: Vector measures, weakly compact operators, Radon-Nikodým property, topological tensor products, weakly compactly generated spaces
Article copyright: © Copyright 1975 American Mathematical Society