Vector measure Maurey-Rosenthal-type factorizations and l-sums of L1-spaces

Consider a vector measure of bounded variation in with values in a Banach space and an operator T : X --> L-1(m), where L-1 (m) is the space of integrable functions with respect to In. We characterize when T can be factorized through the space L-2(m) by means of a multiplication operator given by a function of L-2(\m\), where \m\ is the variation of m, extending in this way the Maurey-Rosenthal Theorem. We use this result to obtain information about the structure of the space L-1(m) when in is a sequential vector measure. In this case the space L-1(m) is an l-sum of L-1-spaces. (C) 2004 Elsevier Inc. All rights reserved.