Weak compactness criteria and convergences in L1E(u)

• Autores: C. Castaing, H. Benabdellah
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 48, Fasc. 4-6, 1997, págs. 423-448
• Idioma: inglés
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• Resumen

  • 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.