FACTORIZATION OF QUASI-DIFFERENTIAL EXPRESSIONS WITH OPERATOR-VALUED COEFFICIENTS

Quasi-differential expressions M with coefficients having values in the space of bounded linear operators of a Banach space E into itself are considered. A result on factorizations of the form M = QP obtained by A. Zettl for scalar differential expressions is generalized to the case of operator-valued coefficients, with a completely different proof, which also gives the coefficients of P and Q explicitly. For reflexive E an extension of a result on factorizations of the form M = RQP proved by P.J. Browne and R. Nillsen for scalar classical expressions is obtained. Finally in case of E being a Hilbert space, a factorization result for symmetric expressions is given, which is attributed to G. Frobenius for scalar classical expressions.