The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of $c_{0}$
Volume 104 / 1993
Studia Mathematica 104 (1993), 111-123
DOI: 10.4064/sm-104-2-111-123
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.
