Infinite Toeplitz and Laurent matrices with localized impurities (Q1348085)

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.