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Shorter Notes: L1 x is Weakly Compactly Generated if x is
Proceedings of the American Mathematical Society
Vol. 48, No. 2 (Apr., 1975), pp. 508-510
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040292
Page Count: 3
You can always find the topics here!Topics: Banach space, Mathematical functions, Topological compactness, Linear transformations, Mathematical vectors
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Though good criteria for weak compactness in the space of Bochner-integrable functions are not yet known, one can show that L1(μ; X) is a weakly compactly generated Banach space whenever μ 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. Pelczynski.
Proceedings of the American Mathematical Society © 1975 American Mathematical Society