Infinite Toeplitz and Laurent matrices with localized impurities
type: Item
instance of: scholarly article
title: Infinite Toeplitz and Laurent matrices with localized impurities
zbMATH Open document ID: 0995.15013
DOI: 10.1016/S0024-3795(01)00343-3
author: V. I. Sokolov
author: A. Böttcher
author: Mark Embree
published in: Linear Algebra and its Applications
publication date: 2002-05-15T00:00:00Z
review text: The change of the spectra of non-scalar infinite Toeplitz and Laurent matrices under perturbations is studied (perturbations in a prescribed set of sites are considered). Such a spectrum is not affected by sufficiently small localized impurities. This robustness of the spectrum is caused by the rigid structure of Toeplitz matrices which is not destroyed outside the block. Impurities can enlarge the spectrum of the corresponding Laurent matrix. The spectra that emerge when Toeplitz or Laurent matrices are perturbed in a randomly chosen single site are also studied.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 81Q15
zbMATH DE Number: 1741657
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: Laurent matrices
zbMATH Keywords: perturbation by impurities
zbMATH Keywords: spectra of matrices
zbMATH Keywords: infinite matrices
MaRDI profile type: Publication
cites work: On the spectra of finite-dimensional perturbations of matrix multiplication operators
cites work: The Asymptotic Spectra of Banded Toeplitz and Quasi-Toeplitz Matrices
cites work: Pseudospectra and singular values of large convolution operators
cites work: Spectral approximation of banded Laurent matrices with localized random perturbations
cites work: The spectra of large Toeplitz band matrices with a randomly perturbed entry
cites work: Introduction to large truncated Toeplitz matrices
cites work: Weyl's theorem for nonnormal operators
cites work: Spectral properties of random non-self-adjoint matrices and operators
cites work: Spectral value sets of closed linear operators
cites work: Spectral value sets: A graphical tool for robustness analysis
cites work: Q3356185
cites work: On Szegö's eigenvalue distribution theorem and non-Hermitian kernels
cites work: Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
cites work: Localized Eigenvectors from Widely Spaced Matrix Modifications
cites work: Pseudospectra of Linear Operators
cites work: Q4938350
cites work: Spectra, pseudospectra, and localization for random bidiagonal matrices
full work available at URL: s0024-3795(01)00343-3
OpenAlex ID: W2036872711
Recommended article: Spectrum localization of infinite matrices
Recommended article: Infinite extensions of Toeplitz matrices
Recommended article: Q5695281
Recommended article: Infinite Toeplitz-Lipschitz matrices and operators
Recommended article: Q4732890
Recommended article: Infinite random matrix theory, tridiagonal bordered Toeplitz matrices, and the moment problem
Recommended article: FIXED POINT THEOREM FOR AN INFINITE TOEPLITZ MATRIX
Recommended article: Finite and infinite structures of rational matrices: a local approach
Recommended article: Q3700325
Recommended article: Infinite-dimensional features of matrices and pseudospectra
description: scientific article; zbMATH DE number 1741657