Czechoslovak Mathematical Journal, Vol. 57, No. 2, pp. 679-688, 2007

Embedding $c_0$ in $\mathop{ bvca}(\Sigma,X)$

J. C. Ferrando, L. M. Sanchez Ruiz

J. C. Ferrando, Centro de Investigacion Operativa, Universidad Miguel Hernandez, E-03202 Elche (Alicante), Spain, e-mail: jc.ferrando@umh.es; L. M. Sanchez Ruiz, Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia, Spain, e-mail: lmsr@mat.upv.es

Abstract: If $(\Omega,\Sigma) $ is a measurable space and $X$ a Banach space, we provide sufficient conditions on $\Sigma$ and $X$ in order to guarantee that $\bvca( \Sigma,X) $, the Banach space of all $X$-valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of $c_0$ if and only if $X$ does.

Keywords: countably additive vector measure of bounded variation, Pettis integrable function space, copy of $c_0$, copy of $\ell_{\infty}$

Classification (MSC 2000): 46G10, 28B05


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