QUADRATIC INTEGRALS AND FACTORIZATION OF LINEAR OPERATORS.

We consider operators on the matrix-valued disc algebra. We show that any bounded linear operator T: A—5’X to a Banach space X of cotype 2 induces a bounded operator G½’X defined on some weighted Bergman space G½ on the unit disc. We give sufficient conditions on the weight ½ for the formal inclusion A—5’G½ to be 2C*-summing. Decompositions of T with respect to operator-valued measures are obtained. [ABSTRACT FROM AUTHOR]