%0 Journal Article
%A Bombal Gordón, Fernando
%T On embedding l 1   as a complemented subspace of Orlicz vector valued function spaces.
%D 1988
%@ 0214-3577
%U https://hdl.handle.net/20.500.14352/57888
%X A Banach space E  is said to have property A [property B] if E  contains a copy isomorphic with l 1 [a complemented subspace isomorphic with l 1 ]. G. Pisier proved that the Lebesgue-Bochner space L p (μ,E) , 1<p<∞ , has property A if E  has the same property. The author of the paper under review extended Pisier's result to the case of Orlicz-Bochner function spaces L Φ (μ,E) , where Φ  is a Young function [the author, Math. Proc. Cambridge Philos. Soc. 101 (1987), no. 1, 107–112;]. In the same paper the author further proved that if E  is a Banach lattice, and Φ  satisfies Δ 2  -condition, and if the measure μ  is nonpurely atomic then L Φ (μ,E)  has property B if and only if L Φ  or E  has property B. In the present paper the author continues to study the problem of characterizing spaces L Φ (μ,E)  with property B, dropping the assumption that E  is a Banach lattice. One such result asserts that if E  has the weak (V ∗ )  property and Φ satisfies the Δ 2  -condition, then L Φ (μ,E)  has property B if and only if L Φ or E  has property B. The author states several results related to the open problem of characterizing completely the spaces L Φ (μ,E)  with property B in terms of properties of E  or L Φ .
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