If $(\Omega,\Sigma,\mu)$ is a finite measure space and $X$ a Banach space, in this note we show that $L_{w^{\ast}}^{1}(\mu,X^{\ast})$, the Banach space of all classes of weak* equivalent $X^{\ast}$-valued weak* measurable functions $f$ defined on $\Omega$ such that $\|f(\omega )\| \leq g(\omega )$ a.e. for some $g\in L_{1}(\mu )$ equipped with its usual norm, contains a copy of $c_{0}$ if and only if $X^{\ast}$ contains a copy of $c_{0}$.
@article{119207,
author = {Juan Carlos Ferrando},
title = {A note on copies of $c\_0$ in spaces of weak* measurable functions},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {41},
year = {2000},
pages = {761-764},
zbl = {1050.46512},
mrnumber = {1800168},
language = {en},
url = {http://dml.mathdoc.fr/item/119207}
}
Ferrando, Juan Carlos. A note on copies of $c_0$ in spaces of weak* measurable functions. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) pp. 761-764. http://gdmltest.u-ga.fr/item/119207/
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