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On joint spectra of non-commuting normal operators

Published online by Cambridge University Press:  17 April 2009

Alan J. Pryde  and
Andrzej Sołtysiak
Alan J. Pryde
Affiliation:
Department of Mathematics, Monash University, Clayton Vic 3168, Australia
Andrzej Sołtysiak
Affiliation:
Institute of Mathematics A. Mickiewicz University Matejki, 48/49, 60769 Poznań, Poland
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The purpose of the paper is to show that the Harte spectrum and the bicommutant spectrum of an arbitrary n−tuple of normal Hilbert space operators can be obtained from the spectral set γ introduced by McIntosh and Pryde. It is also proved that many commonly used joint spectra of an n−tuple of normal m by m matrices are equal. These results are non-commutative variants of some theorems proved by McIntosh, Pryde, and Ricker for commuting sets of operators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 163 - 170
Copyright
Copyright © Australian Mathematical Society 1993

References

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