Inequalities for eigenvalues of compactly perturbed unitary operators

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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.

Original languageEnglish
Article numberOaM-11-32
Pages (from-to)493-503
Number of pages11
JournalOperators and Matrices
Volume11
Issue number2
DOIs
StatePublished - 1 Jun 2017

Keywords

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

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