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Weak compactness in
Authors:Santiago Dí  az
Institution:Departamento de Matemática Aplicada II, Universidad de Sevilla E.S. Ingenieros Industriales, Avda. Reina Mercedes s/n, 41012-Sevilla, Spain
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.

Keywords:Lebesgue-Bochner integrable functions  regular methods of summability  Cesà  ro convergence  weak compactness  Radon-Nikodý  m property
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