A Bauer-Fike theorem for the joint spectrum of commuting matrices

Pryde, A. J.

doi:10.1016/0024-3795(92)90430-i

Cited by 8 publications

(26 citation statements)

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“…In fact, we establish bounds similar to the matrix case given by Pryde [18] and by Bhatia-Bhattacharyya [3] which are inspired by the Bauer-Fike and Henrici bounds for single matrices. This will be done using Clifford analysis.…”

Section: Introductionmentioning

confidence: 92%

“…We are now in a position to give the desired generalization of the results given by Pryde [18] and Bhatia and Bhattacharyya [3]. Following them we first consider perturbations of real spectra then of complex spectra.…”

Section: Henrici Theorem 235mentioning

confidence: 98%

“…Following Pryde [18], to remove the assumption of real spectra, we shall use partitions of tuples of operators. We shall also need the 'spectral mapping theorem' for both the joint spectrum and the joint approximate spectrum.…”

Section: Perturbations Of Tuples With Complex Spectramentioning

confidence: 99%

“…We shall also need the 'spectral mapping theorem' for both the joint spectrum and the joint approximate spectrum. We first recall the definition of a partition [18]. …”

Section: Perturbations Of Tuples With Complex Spectramentioning

confidence: 99%

“…The paper is organized as follows: Following [18], we first give some necessary tools and definitions, then we establish the Henrici theorem for tuples of operators having real spectra. At the end we consider operators with complex spectra.…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 92%

Section: Henrici Theorem 235mentioning

confidence: 98%

Section: Perturbations Of Tuples With Complex Spectramentioning

confidence: 99%

“…We shall also need the 'spectral mapping theorem' for both the joint spectrum and the joint approximate spectrum. We first recall the definition of a partition [18]. …”

Section: Perturbations Of Tuples With Complex Spectramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations