Weak compactness in $L^1(\mu ,X)$
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- by Santiago Díaz
- Proc. Amer. Math. Soc. 124 (1996), 2685-2693
- DOI: https://doi.org/10.1090/S0002-9939-96-03336-9
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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.References
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Bibliographic Information
- Santiago Díaz
- Affiliation: Departamento de Matemática Aplicada II, Universidad de Sevilla E.S. Ingenieros Industriales, Avda. Reina Mercedes s/n, 41012-Sevilla, Spain
- MR Author ID: 310764
- Email: madrigal@cica.es
- Received by editor(s): June 28, 1994
- Received by editor(s) in revised form: February 21, 1995
- Communicated by: Dale Alspach
- © Copyright 1996 American Mathematical Society
- 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