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Weak compactness criteria and convergences in $L^1_E(\mu)$
- Source :
- Collectanea Mathematica; 1997: Vol.: 48 Núm.: 4-6; p. 423-448
- Publication Year :
- 1997
- Publisher :
- Universitat de Barcelona, 1997.
-
Abstract
- New characterizations of conditionally weakly compact (resp. relatively weakly compact) subsets in Banach space $E$ and $L^1_E(\mu)$ are presented. We discuss also several types of convergence in $L^1_E(\mu)$, in particular we generalize Szlenk's theorem on Cesàro norm-convergence of weakly null sequences in $L^1_\mathbb{R}(\mu)$ to the norm-summability with respect to a class of regular method of summability of weakly null sequences in $L^1_H(\mu)$ where $H$ is a Hilbert space.
Details
- Language :
- Catalan; Valencian
- Database :
- OpenAIRE
- Journal :
- Collectanea Mathematica
- Accession number :
- edsair.od.......613..d596525b4b591bd0ecfa078ea253c431