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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

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