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The spectrum of an R-homomorphism

Published online by Cambridge University Press:  09 April 2009

A. W. Wickstead
A. W. Wickstead
Affiliation:
Department of Pure Mathematics, The Queen's University of Belfast, Northern Ireland.
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Abstract

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Let E be a real Banach space ordered by a closed, normal and generating cone. Suppose also that the order induced on E has the Riesz decomposition property. It is shown that if T:E → E is a positive linear operator with the property that y, z, a ∈ E with a ≧ Ty, Tz implies there is x ∈ E with x ≧ y, z and a ≧ Tx then the approximate point spectrum and spectrum of T are cyclic subsets of the complex plane. That is, if α = |α|γ lies in one of these sets then so does |α|γk for all integers k.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 42 - 45
Copyright
Copyright © Australian Mathematical Society 1977

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