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An extension of Henrici theorem for the joint approximate spectrum of commuting spectral operators

Part of: Ordinary differential operators General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Ali Ben Amor
Ali Ben Amor
Affiliation:
Universität BielefeldFakultät für Mathematik 33615 BielefeldGermany e-mail: benamor@mathematik.uni-bielefeld.de
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Abstract

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Given two m-tuples of commuting spectral operators on a Hilbert space, T = (T1,…, Tm) and S = (S1,…, Sm), an extended version of Henrici perturbation theorem is obtained for the joint approximate spectrum of S under perturbation by T. We also derive an extended version of Bauer-Fike theorem for such tuples of operators. The method used involves Clifford algebra techniques introduced by McIntosh and Pryde.

Keywords

spectral operatorjoint spectrumHenrici's bound

MSC classification

Secondary: 47A13: Several-variable operator theory (spectral, Fredholm, etc.) 34L05: General spectral theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 2 , October 2003 , pp. 233 - 246
Copyright
Copyright © Australian Mathematical Society 2003

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