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The non-emptiness of joint spectral subsets of euclidean n-space

Published online by Cambridge University Press:  09 April 2009

W. J. Ricker
Affiliation:
School of Mathematics University of New South WalesP.O. Box 1 Kensington, N.S.W., Australia
A. R. Schep
Affiliation:
Department of Mathematics, University of South Carolina Columbia, South Carolina, U.S.A.
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Abstract

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A.McIntosh and A. Pryde introduced and gave some applications of notion of “spectral set”, γ(T), associated with each finite, commuting family of continuous linear operators T in a Banach space. Unlike most concepts of joint spectrum, the set γ(T) is part of real Euclidean space. It is shown that γ(T) is always non-empty whenver there are at least two operators in T.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1989

References

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