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On Orlicz spaces of vector-valued functions. (Spanish: Sobre los espacios de Orlicz de funciones vectoriales)

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Bombal Gordón, Fernando (1981) On Orlicz spaces of vector-valued functions. (Spanish: Sobre los espacios de Orlicz de funciones vectoriales). Collectanea mathematica, 32 (1). pp. 3-12. ISSN 0010-0757

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Official URL: http://www.collectanea.ub.edu/index.php/Collectanea/article/view/3535/4214




Abstract

Let (S,Σ,μ) be a finite measure space, X a Banach space and Φ a Young function with complementary function Ψ. There is a natural duality between the Orlicz spaces LΦ(X) and LΨ(X∗), given by (f,g)↦∫⟨f,g⟩dμ. Assume that X satisfies the Radon-Nikodým property. One of the main results obtained in this paper is the following: K⊂LΦ(X) is σ(LΦ(X),LΨ(X∗)) relatively sequentially compact if and only if the following conditions are satisfied: (i) K is norm-bounded, (ii) the set K(A)={∫Afdμ:f∈K} is relatively weakly compact in X for every A∈Σ, and (iii) limμ(A)→0sup{∫A⟨f,g⟩dμ:f∈K}=0 for every g∈LΨ(X∗).


Item Type:Article
Uncontrolled Keywords:Radon-Nikodým property;Orlicz spaces;Banach space.
Subjects:Sciences > Mathematics > Differential geometry
ID Code:17980
Deposited On:29 Jan 2013 09:34
Last Modified:02 Aug 2018 07:49

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