Pelczynski's property (V) on spaces of vector valued functions

Abstract

Let $E$ be a separable Banach space and $Ω$ be a compact Hausdorff space. It is shown that the space $C(Ω,E)$ has property (V) if and only if $E$ does. Similar result is also given for Bochner spaces $L^p(μ,E)$ if $1<p<\infty$ and $μ$ is a finite Borel measure on $Ω$.