RT Journal Article
T1 On embedding l 1   as a complemented subspace of Orlicz vector valued function spaces.
A1 Bombal Gordón, Fernando
AB 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 .
PB Editorial de la Universidad Complutense
SN 0214-3577
YR 1988
FD 1988
LK https://hdl.handle.net/20.500.14352/57888
UL https://hdl.handle.net/20.500.14352/57888
LA eng
NO F. BOMBAL, On 11 subspaces of Orlicz vector valued function spaces. Mah. Proc. Cambridge Phil. Soe. (1987), 107-112.F. BOMBAL, On (V*) sets and Pelczynski's property (V*). To appear.F. BOMBAL and C. FIERRO, Compacidad débil en espacios de Orlicz de funciones vectoriales. Reu. Aead. Ci. de Madrid, 78 (1984), 157-163.J. LINDENSTRAUSS and L. TZAFRIRI, Classieal Banaeh Spaees, vol. I. Springer, 1977.J. LINDENSTRAUSS and L. TZAFRIRI, Classieal Banaeh spaees, vol. II. Springer, 1979.A. PELCZYNSKI, On Banach spaces on which every unconditionally converging operator is weakly compact. Bull. Aead. Poi. Sei., 10 (1962), 641-648.G. PISIER, Une proprieté de stabilité de la c1asse des espaces ne contenant pas 11• e. R. Aead. Sei. Paris, Ser. A, 285 (1978), 747-749.C. SAMUEL, Sur la reproducibilite des espaees lP. Seminaire d'analyse fonctionnelle. Ecole Polytechnique, Paris (1978-1979). Exp. XXVI.L. TZAFRIRI, Reflexivity in Banach lattices and their subspaces. J. of Funct. Analysis, 10 (1972), 1-18.A. C. ZAANEN, Linear Analysis. North Holland, 1953.
NO CAICYT
DS Docta Complutense
RD 15 may 2024