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Complemented copies of l1, in Lp(μ;E)

Published online by Cambridge University Press:  24 October 2008

José Mendoza
José Mendoza
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain
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Abstract

Let E be a Banach space, let (Ω, Σ, μ) a finite measure space, let 1 < p < ∞ and let Lp(μ;E) the Banach space of all E-valued p-Bochner μ-integrable functions with its usual norm. In this note it is shown that E contains a complemented subspace isomorphic to l1 if (and only if) Lp(μ; E) does. An extension of this result is also given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 3 , May 1992 , pp. 531 - 534
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

[1]Bombal, F.. On l 1, subspaces of Orlicz vector-valued function spaces. Math. Proc. Cambridge Philos. Soc. 101 (1987), 107–112.CrossRefGoogle Scholar
[2]Bombal, F.. On embedding l 1 as a complemented subspace of Orlicz vector valued function spaces. Rev. Mat. Univ. Complutense Madrid 1 (1988), 13–17.Google Scholar
[3]Bombal, F.. On (V*) sets and Pelczynski's property (V*). Glasgow Math. J. 32 (1990), 109–120.CrossRefGoogle Scholar
[4]Bourgain, J.. New classes of Lp-spaces. Lecture Notes in Math. vol. 889 (Springer-Verlag, 1981).Google Scholar
[5]Diestel, J.. Sequences and Series in Banach spaces. Graduate Texts in Math. no. 92 (Springer-Verlag, 1984).CrossRefGoogle Scholar
[6]Diestel, J. and Uhl, J. J. Jr. Vector Measures. Math. Surveys no. 15 (American Mathematical Society, 1977).CrossRefGoogle Scholar
[7], A. and Tulcea, C. Ionescu. Topics in the Theory of Liftings. Ergebnisse der Mathematik und ihrer Grenzgebiete vol. 48 (Springer-Verlag, 1969).Google Scholar
[8]Lindenstauss, J. and Tzafriri, L.. Classical Banach spaces, vol. 1. Ergebnisse der Mathematik und ihrer Grenzgebiete vol. 92 (Springer-Verlag, 1977).CrossRefGoogle Scholar
[9]Lindenstauss, J. and Tzafriri, L.. Classical Banach spaces, vol. 2. Ergebnisse der Mathematik und ihrer Grenzgebiete vol. 97 (Springer-Verlag, 1979).CrossRefGoogle Scholar
[10]Pisier, G.. Une proprieté de stabilité de la classe des espaces ne contenant pas l 1. C.R. Acad. Sci. Paris Sér. A 286 (1978), 747–749.Google Scholar
[11]Talagrand, M.. Weak Cauchy sequences in L 1(E). Amer. J. Math. 106 (1984), 703–724.CrossRefGoogle Scholar
[12]Tzafriri, L.. Reflexivity in Banach lattices and their subspaces. J. Funct. Anal. 10 (1972), 1–18.CrossRefGoogle Scholar