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Factorization of Quasi‐Differential Expressions with Operator‐Valued Coefficients
Author(s) -
Frentzen Hilbert
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/50.1.139
Subject(s) - mathematics , scalar (mathematics) , factorization , bounded function , pure mathematics , differential operator , hilbert space , extension (predicate logic) , mathematical analysis , geometry , algorithm , computer science , programming language
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.