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Complemented copies of L1 in Lp(μ;E).

Mendoza Casas, José (1992) Complemented copies of L1 in Lp(μ;E). Mathematical Proceedings of the Cambridge Philosophical Society, 111 (3). pp. 531-534. ISSN 0305-0041

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Abstract

Let E be a Banach space, let (OMEGA, SIGMA, mu) a finite measure space, let 1 < p < infinity and let L(p)(mu; E) the Banach space of all E-valued p-Bochner mu-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 ) L(p)(mu; E) does. An extension of this result is also given.


Item Type:Article
Uncontrolled Keywords:block sequence; finite measure space; complemented subspace
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16886
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Last Modified:13 Nov 2013 16:32

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