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On (V*) sets in Bochner integrable function spaces



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Bombal Gordón, Fernando (1991) On (V*) sets in Bochner integrable function spaces. Atti del Seminario matematico e fisico dell'Università di Modena, 39 (1). pp. 165-169. ISSN 0041-8986


A subset A of a Banach space E is called a (V*) -set if, for every weakly unconditionally Cauchy (w.u.c.) series ∑x ∗ n in E ∗ , lim n→∞ sup a∈A |x ∗ n (a)|=0 . Following Pełczyński, a Banach space E is said to have property (V*) if every (V*)-set in E is relatively weakly compact. The paper under review is mainly a survey of all known results connected with property (V*) and with another property that the author introduced and called weak (V*) , where a Banach space E is said to have weak (V*) if (V*)-sets in E are weakly conditionally compact

Item Type:Article
Uncontrolled Keywords:(V*)-set; weakly unconditionally Cauchy series; weak-(V*)- property
Subjects:Sciences > Mathematics > Topology
ID Code:19890
Deposited On:11 Feb 2013 15:16
Last Modified:11 Feb 2013 15:16

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