Multiple 2-summing operators from a Cartezian product of l1(H)-spaces with values in a Hilbert space.

We use the Maurey–Rosenthal factorization theorem to give the necessary and sufficient conditions that an operator on the Cartezian product of $ l_{1}\left (H\right) $ l 1 (H) -spaces with values in a Hilbert space to be multiple 2-summing. Various applications of this characterization are given. [ABSTRACT FROM AUTHOR]