Spectral stability for compact perturbations of Toeplitz matrices

Abstract

Let f be a regular real-valued non-constant symbol defined on the one dimensional torus T. Denote respectively by κ and T, its set of critical points and the associated Toeplitz matrix on l2(N). If V is a suitable compact perturbation, we prove that the operator T+V has no singular continuous spectrum and only finite point spectrum away from the set of thresholds f(κ). We also obtain some propagation estimates and apply these results to concrete examples.