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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$L^{1}_{x}$ is weakly compactly generated if $X$ is
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by J. Diestel PDF
Proc. Amer. Math. Soc. 48 (1975), 508-510 Request permission

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.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 508-510
  • MSC: Primary 46E40; Secondary 46B05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0367651-X
  • MathSciNet review: 0367651