Spectrum localization of a perturbed operator in a strip and applications

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Abstract

Let A and à be bounded operators in a Hilbert space. We consider the following problem: let the spectrum of A lie in some strip. In what strip the spectrum of à lies if A and à are “close”? Applications of the obtained results to integral operators and matrices are also discussed. In addition, we apply our perturbation results to approximate the spectral strip of a Hilbert-Schmidt operator by the spectral strips of finite matrices.

Original languageEnglish
Pages (from-to)395-412
Number of pages18
JournalOpuscula Mathematica
Volume41
Issue number3
DOIs
StatePublished - 1 Jan 2021

Keywords

  • Approximation
  • Integral operator
  • Matrix
  • Operator
  • Perturbation
  • Spectrum

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