1. WELL-BOUNDEDNESS OF SUMS AND PRODUCTS OF OPERATORS.
- Author
-
IAN DOUST and T. A. GILLESPIE
- Subjects
OPERATOR functions ,FUNCTIONS of bounded variation ,SCALAR field theory ,BANACH spaces ,GENERALIZED spaces - Abstract
A sufficient condition is given under which the sum, product and indeed any polynomial combination of a well-bounded operator and a commuting real scalar-type spectral operator is well-bounded. This generalizes a result of Gillespie for Hilbert space operators. It is shown in particular that if $X$ is a UMD space, then the sum of finitely many commuting real scalar-type spectral operators acting on $X$ is a well-bounded operator (a result which fails on general reflexive Banach spaces). [ABSTRACT FROM AUTHOR]
- Published
- 2003
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