Variations of real and imaginary parts of eigenvalues of compact operators under perturbations

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1 Scopus citations

Abstract

Let A and S be compact operators in a Hilbert space, and S be selfadjoint. Under certain conditions we derive bounds for the quantities supkinfj|Reλk(A)-λj(S)| and supkinfj|Imλk(A)-λj(S)| , where λk(A) (k= 1 , 2 ,..) are the eigenvalues of A. We also discuss applications of the obtained bounds to the theory of Jacobi and Schatten–von Neumann operators.

Original languageEnglish
Article number61
JournalAnalysis and Mathematical Physics
Volume13
Issue number4
DOIs
StatePublished - 1 Aug 2023

Keywords

  • Compact operators
  • Hilbert space
  • Jacobi operator
  • Perturbations
  • Schatten–von Neumann operator

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics

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