On the space Lp(μ,X). (Spanish: Sobre el espacio Lp(μ,X)).



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Bombal Gordón, Fernando (1980) On the space Lp(μ,X). (Spanish: Sobre el espacio Lp(μ,X)). Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid, 74 (1). pp. 131-135. ISSN 0034-0596

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Letting X be a Banach space, (S,μ,Σ) a space of finite measure, 1<p<∞ , and L p (μ,X) the space of functions from S into X with |f| p integrable, the author studies the dual pair (L p (μ,X),L q (μ,X ′ )). He gives necessary conditions, which are also sufficient if X has the Radon-Nikodým property, in order that a subset of L p (μ,X) be σ(L p (μ,X),L q (μ,X ′ )) -relatively sequentially compact and shows that L p (μ,X) is σ(L p (μ,X),L q (μ,X ′ )) sequentially complete for every finite measure μ if and only if X is weakly sequentially complete and has the Radon-Nikodým property.

Item Type:Article
Uncontrolled Keywords:Lp-spaces; Orlicz spaces; Köthe function spaces; Lorentz spaces; rearrangement invariant spaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Differential equations
ID Code:17971
Deposited On:25 Jan 2013 09:46
Last Modified:02 Aug 2018 07:50

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