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Proceedings of the American Mathematical Society

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

 

 

Weak compactness in $L^{1}(\mu ,X)$


Author: Santiago Díaz
Journal: Proc. Amer. Math. Soc. 124 (1996), 2685-2693
MSC (1991): Primary 46B25, 46E40
DOI: https://doi.org/10.1090/S0002-9939-96-03336-9
MathSciNet review: 1327006
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Abstract: We characterize weak compactness and weak conditional compactness of subsets of $L^{1}(\mu ,X)$ in terms of regular methods of summability. We also study when these results still hold using only convergence in the sense of Cesàro.


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Santiago Díaz
Affiliation: Departamento de Matemática Aplicada II, Universidad de Sevilla E.S. Ingenieros Industriales, Avda. Reina Mercedes s/n, 41012-Sevilla, Spain
Email: madrigal@cica.es

DOI: https://doi.org/10.1090/S0002-9939-96-03336-9
Keywords: Lebesgue-Bochner integrable functions, regular methods of summability, Cesàro convergence, weak compactness, Radon-Nikodým property
Received by editor(s): June 28, 1994
Received by editor(s) in revised form: February 21, 1995
Communicated by: Dale Alspach
Article copyright: © Copyright 1996 American Mathematical Society