Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-29T14:13:03.582Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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