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WELL-BOUNDEDNESS OF SUMS AND PRODUCTS OF OPERATORS

Published online by Cambridge University Press:  08 August 2003

IAN DOUST  and
T. A. GILLESPIE
IAN DOUST
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, [email protected]
T. A. GILLESPIE
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Edinburgh EH9 3JZ [email protected]
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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).

Keywords

47B40
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 183 - 192
Copyright
The London Mathematical Society 2003

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