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

Part of: General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

W. J. Ricker  and
A. R. Schep
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

Secondary: 47A10: Spectrum, resolvent
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 2 , October 1989 , pp. 300 - 306
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Mcintosh, A. and Pryde, A., ‘The solution of systems of operator equations using Clifford algebras’, Proc. Centre Math. Anal., vol. 9, pp. 212–222 (Australian National University, Canberra, 1985).Google Scholar
[2]Mcintosh, A., ‘Clifford algebras and applications in analysis’, Lectures at the University of N.S.W. University of Sydney, joint analysis seminar, 1985.Google Scholar
[3]McIntosh, A. and Pryde, A., ‘A functional calculus for several commuting operators’, Indiana Univ. Math. J. 36 (1987), 421–439.CrossRefGoogle Scholar
[4]McIntosh, A., Pryde, A. and Ricker, W. J., ‘Comparison of joint spectra for certain classes of commuting operators’, Studia Math. 88 (1988), 23–36.CrossRefGoogle Scholar
[5]Ricker, W. J., ‘“Spectral subsets” of Rm assoiciated with commuting families of linear operators’, North-Holland Math. Studies 150 (1988), 243–247.CrossRefGoogle Scholar