Operator ideal properties of the integration map of a vector measure

Let mm be a vector measure with values in a Banach space XX. We explore the relationship between operator ideal properties of the integration map Im:f↦∫fdm from L1(m)L1(m) to XX, and properties of the vector measure mm. For instance, membership of ImIm in certain operator ideals implies that L1(m)=L1(|m|)L1(m)=L1(|m|), where |m||m| is the variation measure of mm. This happens, for example, if ImIm is compact, or pp-summing or in certain cases, completely continuous. Characterizations of when ImIm is compact or absolutely summing are also given. For many operator ideals, membership of ImIm is determined solely by the range of mm.