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A functional calculus for continuous affine operators

Published online by Cambridge University Press:  17 April 2009

J.J. Koliha
J.J. Koliha
Affiliation:
Department of Mathematics, University of Melbourne, Parkvilie, Victoria.
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Abstract

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In the Appendix to a recent paper by J.J. Koliha and A.P. Leung (Math. Ann.216 (1975), 273–284), a functional calculus for continuous affine operators was constructed on the basis of the Taylor-Dunford calculus. This calculus applied only to functions defined and analytic in an open set containing the spectrum of an operator and the point λ = 1. In the present paper I examine the affine resolvent, and develop independently a more general calculus applicable to functions which are analytic in any open neighbourhood of the spectrum of an affine operator.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 2 , April 1976 , pp. 279 - 288
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Ahlfors, Lars V., Complex analysis: an introduction to the theory of analytic functions of one complex variable, second edition (McGraw-Hill, New York; Toronto, Ontario; London; 1966).Google Scholar
[2]Hille, Einar and Phillips, Ralph S., Functional analysis and semigroups (Colloquium Publications, 31, revised edition. Amer. Math. Soc., Providence, Rhode Island, 1957).Google Scholar
[3]Koliha, J.J. and Leung, A.P., “Ergodic families of affine operators”, Math. Ann. 216 (1975), 273–28.CrossRefGoogle Scholar