Comparison of joint spectra for certain classes of commuting operators

McIntosh, Alan; Pryde, A. J.; Ricker, Werner J.

doi:10.4064/sm-88-1-23-36

Cited by 29 publications

(23 citation statements)

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“…This means that if k e Sp (7), then (Re(X), Im(X)) € Sp(7r (7), where Re(£), lm(P) are respectively the real and the imaginary parts of p. It is also known [15] that every tuple of commuting spectral operators has an admissible partition. Thus using this results one can carry over Proposition 3.2 to arbitrary tuples consisting of commuting spectral operators.…”

Section: (Y(n(t)))mentioning

confidence: 99%

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

Amor

2003

J. Aust. Math. Soc.

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Given two m-tuples of commuting spectral operators on a Hilbert space, T = (T\,... ,T m ) and 5 = (Si S m ), 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 Mclntosh and Pryde.2000 Mathematics subject classification: primary 47 A13; secondary 34L05.

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Section: (Y(n(t)))mentioning

confidence: 99%

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

Amor

2003

J. Aust. Math. Soc.

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“…McIntosh, Pryde and Ricker [McIntosh et al 1988] proved that for the k-tuple of commuting bounded generalized scalar operators, the spectrum σ (T ) coincides with many known joint spectra of the (T 1 , . .…”

Section: The Support Of the Functional Calculusmentioning

confidence: 99%

A functional calculus for unbounded generalized scalar operators on Banach spaces

Kečkić¹,

Krtinić²

2011

Pacific J. Math.

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“…Davis [6] drew special attention to this problem and its importance; after that Mcintosh and Pryde [10] introduced a novel idea, the use of Clifford algebras, to develop a functional calculus for commuting tuples of operators and used this to extend earlier perturbation results from [4]. This approach was developed further by them and Ricker [11].…”

Section: Introductionmentioning

confidence: 99%