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Well-boundedness of sums and products of operators

J. London Math. Soc. (2), 68 (2003), 183-192.

Ian Doust and T.A. Gillespie

Address: School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia

Email:  i.doust@unsw.edu.au

Abstract: We give a sufficient condition 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. We show in particular that if X is a UMD space, then the sum of n commuting real scalar-type spectral operators acting on $X$ is a well-bounded operator (a result which fails on general reflexive Banach spaces).

Key words and phrases. Well-bounded operators, scalar-type spectral operators.

2000 Mathematics Subject Classification. Primary 47B40.

This paper appeared in the Journal of the London Mathematical Society, which is available (to subscribers) online.

Bibliographic reference:
I. Doust and T. A. Gillespie, Well-boundedness of sums and products of operators, J. London Math. Soc. (2) 68 (2003), no. 1, 183--192; MR 2004a:47032

The preprint (dated 23/07/02), which may differ from the final version in the journal, is available in several forms:

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