When does $\textrm {ca}(\Sigma ,X)$ contain a copy of $l_ \infty$ or $c_ 0$?

Abstract:

For a $\sigma$-algebra $\Sigma$ and a Banach space $X,ca\left ( {\Sigma ,X} \right )$ is the Banach space of all vector measures from $\Sigma$ to $X$. If $\Sigma$ admits a nonzero atomless finite positive measure, then $ca\left ( {\Sigma ,X} \right ) \supset {l_\infty }$ (or ${c_0}$) if and only if there is a noncompact bounded linear operator from ${l_2}$ to $X$ (Theorem 1). Otherwise, $ca\left ( {\Sigma ,X} \right ) \supset {l_\infty }$ (or ${c_0}$) if and only if $X \supset {l_\infty }$ (or ${c_0}$) (Theorem 2).