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oai:docta.ucm.es:20.500.14352/576582023-08-28T05:41:39Zcom_20.500.14352_14col_20.500.14352_15

Copies of l∞ in Lp(μ;X). Mendoza Casas, José 517.5 Bochner-integrable functions Análisis funcional y teoría de operadores Let (Ω,Σ,μ) be any measure space, X a Banach space and for 1≤p<+∞ let Lp(μ,X) be the Banach space of all X-valued Bochner "pth power integrable'' functions on Ω, with the usual "Lp''-norm. A natural question is: do properties enjoyed by Lp(μ,X) "descend'' to X? In the present paper it is proved that Lp(μ,X) contains l∞ isomorphically (if and) only if X does. In a sense, the author's result completes earlier ones [e.g., S. Kwapien, Studia Math. 52 (1974), 187–188; G. Pisier, C. R. Acad. Sci. Paris Sér. A 286 (1978), no. 17, 747–749; ; L. Drewnowski, "Copies of l∞ in the operator spaces Kω∗(X∗,Y)'', to appear]. The proof of the theorem is achieved by applying three earlier results; one is from the paper of Drewnowski [op. cit.], and the other two from a paper by H. P. Rosenthal [Studia Math. 37 (1970), 13–36]. Another recent paper by Drewnowski ["When does ca(Σ,X) contain a copy of l∞ or c0?'', Proc. Amer. Math. Soc., to appear] is also relevant to the present paper. Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T17:01:58Z 2023-06-20T17:01:58Z 1990-05 journal article https://hdl.handle.net/20.500.14352/57658 0002-9939 10.2307/2048371 eng restricted access application/pdf American Mathematical Society