On l 1 subspaces of Orlicz vector-valued function spaces.

dc.contributor.authorBombal Gordón, Fernando
dc.description.abstractThe author studies those Orlicz vector-valued function spaces that contain a copy or a complemented copy of l 1 . Precisely, given a finite complete measure space (S,Σ,μ) , a Young function Φ , and a Banach space E , let L Φ (S,Σ,μ,E) denote the vector space of all (classes of) strongly measurable functions f from S to E such that ∫Φ(k∥f∥)dμ<∞ for some k>0 , and let L Φ (μ)=L Φ (S,Σ,μ,R) . The author first extends a result of G. Pisier concerning vector-valued L p function spaces by showing that if l 1 embeds in L Φ (S,Σ,μ,E) , then l 1 embeds either in L Φ (μ) or in E . This result, combined with a result of E. Saab and the reviewer concerning the embedding of l 1 as a complemented subspace of the Banach space of all E -valued continuous functions on a compact Hausdorff space, is used to show that if in addition E is a Banach lattice, if Φ satisfies the Δ 2 -condition and if μ is nonpurely atomic, then L Φ (S,Ω,μ,E) contains a complemented copy of l 1 if and only if either L Φ (μ) or E contains a complemented copy of l 1
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.identifier.citationBombal, F. and Fierro., C. Compacidad débil en espacios de Orlicz de funciones vectoriales. Rev. Acad. Cienc. Madrid, 78 (1984), 157–163. Diestel, J. and Uhl, J. J. Jr, Vector Measures. Math. Surveys no. 15 (American Mathematical Society, 1977). Dinculeanu., N. Vector measures (Pergamon Press, 1967). Figiel, F., Ghoussoub, N. and Johnson., W. B. On the structure of non-weakly compact operators on Banach lattices. Math. Ann. 257 (1981), 317–334. Halmos., P. R. Measure theory (Van Nostrand Reinhold, 1969). Hernández, F. L. and Peirats., V. A remark on vector sequence F-spaces λ(E) containing a copy of lv. To appear. Kantorovitch, L. and Akilov., G. Analyse fonctionnelle, tome 1 (Mir, Moscow, 1981). Lindenstrauss, J. and Tzafriri., L. On Orlicz sequence spaces: III. Israel J. Math. 14 (1973), 368–384. Lindenstrauss, J. and Tzafriri., L. Classical Banach Spaces, vol. i (Springer, 1977). Lindenstrauss, J. and Tzafriri., L. Classical Banach Spaces, vol. ii (Springer, 1979). Nicolescu., C. Weak compactness in Banach lattices. J. Operator Theory, 6 (1981), 217–281. Pełczyński., A. Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Acad. Polon. Sci. 12 (1962), 641–648. Pisier., G. Une propriété de stabilité de la classe des eapaces ne contenant pasll. C. R. Acad. Sci. Paris Sér. A 286 (1978), 747–749. Saab, E. and Saab., P. A stability property of a class of Banach spaces not containing a complemented copy of l1. Proc. Amer. Math. Soc. 84 (1982), 44–46. Tzapriri., L. Reflexivity in Banach lattices and their subspaces. J. Funct. Analysis 10 (1972), 1–18. Zaanen., A. C. Linear Analysis (North-Holland, 1953).
dc.journal.titleMathematical Proceedings of the Cambridge Philosophical Society
dc.publisherCambridge Univ Press
dc.rights.accessRightsrestricted access
dc.subject.keywordOrlicz vector-valued
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleOn l 1 subspaces of Orlicz vector-valued function spaces.
dc.typejournal article
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