The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$

L. Drewnowski; G. Emmanuele

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ArticleOriginal scientific text

Title

The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$

Authors ¹, ²

Affiliations

Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy

Abstract

Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of

c_{0}

. Then the Bochner space

L^{1} (m; X)

is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.

Keywords

ENG

Banach space, isomorphic copy of

c_{0}

, spaces of vector measures, Bochner integrable functions, Radon-Nikodym property, uncomplemented subspace

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Title

The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of c0

Affiliations

Abstract

Keywords

Bibliography

The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$