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Embedding \(c_{0}\) in \(\operatorname {bvca}(\Sigma ,X)\). (English) Zbl 1174.46016

Summary: 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 \(\operatorname {bvca}( \Sigma ,X) \), 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.

MSC:

46E27 Spaces of measures
46B25 Classical Banach spaces in the general theory
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References:

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