Weakly sequentially complete Orlicz spaces of vector functions. (Spanish: Espacios de Orlicz de funciones vectoriales débilmente secuencialmente completos).

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