Publication: On the space Lp(μ,X). (Spanish: Sobre el espacio Lp(μ,X)).
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Publication Date
1980
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Real Academia de Ciencias Exactas, Físicas y Naturales
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Abstract
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.
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BATT, J. 1974. On weak compactness in spaces of vector-valued measures and Bochner-integrable functions in connection with the Radon-Nikodym property of Banach spaces. «Rev. Roum. Math. Pures et Appi.», XIX, 285-304.
DiESTEL,J.and UHL,J.J.1977.Vector Measures.«Math. Surveys», n.° 15. «Amer. Math. Soc.», Providence, R. I.
DINCULEANU, N. 1967. Vector Measures. Pergamon Press.
DUNFORD, N. and SCHWARTZ, J. T. 1966. Linear Operators,
Part I. Interscience Pub. New York.
FIERRO, C. Tesis doctoral. En elaboración.