@Article{Gil2021,
author = "Gil', Michael",
title = "Spectrum localization of a perturbed operator in a strip and applications",
journal = "Opuscula Math.",
year = "2021",
volume = "41",
number = "3",
pages = "395--412",
doi = "https://doi.org/10.7494/OpMath.2021.41.3.395",
url = "https://doi.org/10.7494/OpMath.2021.41.3.395",
abstract = "Let \(A\) and \(\tilde{A}\) 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 \(\tilde{A}\) lies if \(A\) and \(\tilde{A}\) 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.",
keywords = "operator, spectrum, perturbation, approximation, integral operator, matrix",
issn = "1232-9274"
}