Inequalities for eigenvalues of compactly perturbed unitary operators

Michael Gil

doi:10.7153/oam-11-32

Inequalities for eigenvalues of compactly perturbed unitary operators

Michael Gil

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider the operator A=U +K, where U is a unitary operator and K is a compact one. An eigenvalue λ of A is said to be a non-unitary one, if |λ| ≠1. We derive inequalities for sums of absolute values of the non-unitary eigenvalues. Applications of these inequalities to operator functions, spectrum perturbations and operator equations are also discussed.

Original language	English
Article number	OaM-11-32
Pages (from-to)	493-503
Number of pages	11
Journal	Operators and Matrices
Volume	11
Issue number	2
DOIs	https://doi.org/10.7153/oam-11-32
State	Published - 1 Jun 2017

Keywords

Eigenvalues
Hilbert space
Inequalities Schatten - von Neumann operators
Operator functions
Resolvent
Spectrum perturbations
Sylvester operator equations

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.7153/oam-11-32

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abstract = "We consider the operator A=U +K, where U is a unitary operator and K is a compact one. An eigenvalue λ of A is said to be a non-unitary one, if |λ| ≠1. We derive inequalities for sums of absolute values of the non-unitary eigenvalues. Applications of these inequalities to operator functions, spectrum perturbations and operator equations are also discussed.",

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N2 - We consider the operator A=U +K, where U is a unitary operator and K is a compact one. An eigenvalue λ of A is said to be a non-unitary one, if |λ| ≠1. We derive inequalities for sums of absolute values of the non-unitary eigenvalues. Applications of these inequalities to operator functions, spectrum perturbations and operator equations are also discussed.

AB - We consider the operator A=U +K, where U is a unitary operator and K is a compact one. An eigenvalue λ of A is said to be a non-unitary one, if |λ| ≠1. We derive inequalities for sums of absolute values of the non-unitary eigenvalues. Applications of these inequalities to operator functions, spectrum perturbations and operator equations are also discussed.

KW - Eigenvalues

KW - Hilbert space

KW - Inequalities Schatten - von Neumann operators

KW - Operator functions

KW - Resolvent

KW - Spectrum perturbations

KW - Sylvester operator equations

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M1 - OaM-11-32

ER -

Inequalities for eigenvalues of compactly perturbed unitary operators

Abstract

Keywords

ASJC Scopus subject areas

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