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Journal of the London Mathematical Society 1994 50(1):139-156; doi:10.1112/jlms/50.1.139
© 1994 by London Mathematical Society
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© The London Mathematical Society

Factorization of Quasi-Differential Expressions with Operator-Valued Coefficients

Hilbert Frentzen

Fachbereich 6 – Mathematik und Informatik, Universität GHS Essen, Universitätsstrasse 3 D-45141 Essen, Germany

Received 3 November 1992.

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.


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