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Modified cauchy kernels and functional calculus for operators on Banach space

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Edwin Franks
Edwin Franks
Affiliation:
Depart of Mathematics Macquarie UniversityNSW 2109Australia e-mail: edwin@mpce.mq.edu.au
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Abstract

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In Banach space operators with a bounded H∞ functional calculus, Cowling et al. provide some necessary and sufficient conditions for a type-ω operator to have a bounded H∞ functional calculus. We provide an alternate development of some of their ideas using a modified Cauchy kernel which is L1 with respect to the measure ]dz]/]z]. The method is direct and has the advantage that no transforms of the functions are necessary.

Keywords

functional calculusmatricial functional calculus.

MSC classification

Secondary: 47A60: Functional calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 1 , August 1997 , pp. 91 - 99
Copyright
Copyright © Australian Mathematical Society 1997

References

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