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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Santiago Díaz
Journal: Proc. Amer. Math. Soc. 124 (1996), 2685-2693.
MSC (1991): Primary 46B25, 46E40
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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Additional Information:

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: 10.1090/S0002-9939-96-03336-9
PII: S 0002-9939(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
Copyright of article: Copyright 1996, American Mathematical Society

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