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On joint spectra of non-commuting hyponormal operators

Published online by Cambridge University Press:  17 April 2009

A. Sołtysiak
A. Sołtysiak
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Matejki 48/49, 60–769 Poznań, Poland e-mail: asoltys@amu.edu.pl
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Abstract

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We show that the left joint spectrum of an arbitrary n-tuple of hyponormal Hilbert space operators can be obtained from the spectral set γ introduced by McIntosh and Pryde. A dual statement for cohyponormal operators is also true. The result is a generalisation of a theorem proved by Pryde and the author for normal operators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 131 - 136
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Dash, A.T., ‘Joint essential spectra’, Pacific J. Math. 64 (1976), 119–128.CrossRefGoogle Scholar
[2]Halmos, P.R., A Hilbert Space problem book (Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[3]Harte, R.E., ‘Spectral mapping theorems’, Proc. Roy. Irish Acad. Sect. A 72 (1972), 89–107.Google Scholar
[4]McIntosh, A.G.R. and Pryde, A.J., ‘The solution of systems of operator equations using Clifford algebras’, Proc. Centre Math. Anal. Austral. Nat. Univ. 9 (1985), 212–220.Google Scholar
[5]McIntosh, A.G.R. and Pryde, A.J., ‘A functional calculus for several commuting operators’, Indiana Univ. Math. J. 36 (1987), 421–439.CrossRefGoogle Scholar
[6]McIntosh, A.G.R., Pryde, A. J., and Ricker, W. J., ‘Comparison of joint spectra for certain classes of commuting operators’, Studia Math. 88 (1988), 23–36.CrossRefGoogle Scholar
[7]Pryde, A. J. and Sołtysiak, A., ‘Joint spectra of non-commuting normal operators’, Bull. Austral. Math. Soc. 48 (1993), 163–170.CrossRefGoogle Scholar