MODIFIED CAUCHY-KERNELS AND FUNCTIONAL-CALCULUS FOR OPERATORS ON BANACH-SPACE

Authors
FRANKS E
Citation
E. Franks, MODIFIED CAUCHY-KERNELS AND FUNCTIONAL-CALCULUS FOR OPERATORS ON BANACH-SPACE, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 63, 1997, pp. 91-99
Citations number
9
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
63
Year of publication
1997
Part
1
Pages
91 - 99
Database
ISI
SICI code
0263-6115(1997)63:<91:MCAFFO>2.0.ZU;2-4
Abstract
In Banach space operators with a bounded H-infinity functional calculu s, Cowling et al. provide some necessary and sufficient conditions for a type-omega operator to have a bounded H-infinity functional calculu s. We provide an alternate development of some of their ideas using a modified Cauchy kernel which is L-1 with respect to the measure \dz\/\ z\. The method is direct and has the advantage that no transforms of t he functions are necessary.