Geodesic
A note on copies of $c_0$ in spaces of weak* measurable functions
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 761-764

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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 $c_{0}$.
Classification : 46B20, 46E40, 46G10
Keywords: weak* measurable function; copy of $c_0$; copy of $\ell_1$ 
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     title = {A note on copies of $c_0$ in spaces of weak* measurable functions},
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Ferrando, J. C. A note on copies of $c_0$ in spaces of weak* measurable functions. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 761-764. http://geodesic.mathdoc.fr/item/CMUC_2000__41_4_a8/