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Proceedings of the American Mathematical Society

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

 

 

On weak compactness in $ L\sp 1(\mu, X)$


Authors: J. Diestel, W. M. Ruess and W. Schachermayer
Journal: Proc. Amer. Math. Soc. 118 (1993), 447-453
MSC: Primary 46E40
DOI: https://doi.org/10.1090/S0002-9939-1993-1132408-X
MathSciNet review: 1132408
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Abstract: We present a characterization of weak compactness in $ {L^1}(\mu ,X)$ and in more general Banach spaces of vector-valued measurable functions. Moreover, we slightly refine Talagrand's parametrized version of Rosenthal's $ {l^1}$-theorem and extend it to $ {L^1}(\mu ,X)$-bounded sequences.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1132408-X
Keywords: Bochner integrable functions, weak compactness
Article copyright: © Copyright 1993 American Mathematical Society