Open AccessSpectrum localization of a perturbed operator in a strip and applications
Author(s) -
Michael Gil
Publication year - 2021
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2021.41.3.395
Subject(s) - mathematics , hilbert space , spectrum (functional analysis) , strips , bounded function , operator (biology) , bounded operator , perturbation (astronomy) , spectral theory , mathematical analysis , operator theory , pure mathematics , hilbert transform , operator matrix , essential spectrum , spectral density , quantum mechanics , physics , algorithm , biochemistry , chemistry , statistics , repressor , transcription factor , gene
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.