Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property

Lech Drewnowski

Displaying similar documents to “Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property”

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 (1993)

Studia Mathematica

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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.