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

Drewnowski, L.; Emmanuele, G.

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

c_{0}

Drewnowski, L. ; Emmanuele, G.

Studia Mathematica, Tome 104 (1993), p. 111-123 / Harvested from The Polish Digital Mathematics Library

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Résumé

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.

Publié le : 1993-01-01

Zbl 0811.46038

EUDML-ID : urn:eudml:doc:215963

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Drewnowski, L.; Emmanuele, G. 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) pp. 111-123. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv104i2p111bwm/

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