Geodesic
The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$
Studia Mathematica, Tome 104 (1993) no. 2, pp. 111-123

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-104-2-111-123
Keywords: Banach space, isomorphic copy of $c_0$, spaces of vector measures, Bochner integrable functions, Radon-Nikodym property, uncomplemented subspace

L. Drewnowski 1 ;  1

1 
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L. Drewnowski;  . The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$. Studia Mathematica, Tome 104 (1993) no. 2, pp. 111-123. doi: 10.4064/sm-104-2-111-123

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