Publication: Weakly sequentially complete Orlicz spaces of vector functions. (Spanish: Espacios de Orlicz de funciones vectoriales débilmente secuencialmente completos).
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Publication Date
1986
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Real Academia de Ciencias Exactas, Físicas y Naturales
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Abstract
Extending a theorem of S. Kwapień [Studia Math. 52 (1974), 187–188; the author proves that if E is a Banach space and (S,Σ,μ) is a probability space on which a Bernoulli sequence can be defined, then E contains a subspace isomorphic to c0 if and only if for each Orlicz function φ the space Lφ(S,μ,E) contains a subspace isomorphic to c0. Further, he proves that if E is a weakly sequentially complete Banach lattice, then Lφ(S,μ,E) is weakly sequentially complete for each φ satisfying a certain condition
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HOFFMAN-JORGENSEN, J .Sums of independent Banach space valued random variables. StudiaMath., 52,159-186. (1974).
KRASNOSELSKI, M. A and RUTICKI, Y B.. Convex fundios and Orlicz spaces. Noordhoff., (1961).
KWAPIEN, S.: On Banach spaces containing c0 StudiaMath., 52, 187-188. (1974).
LlNDENSTRAUSS, J. and TZAFRIRI, L.. Classical Banach Spaces II. Springer. (1979).
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