Spectral and scattering theory for perturbed block Toeplitz operators

TL;DR

This paper investigates the spectral properties of perturbed block Toeplitz operators, establishing key results like the limiting absorption principle, absence of singular continuous spectrum, and wave operators using Mourre theory.

Contribution

It introduces a novel approach to analyze spectral properties of perturbed block Toeplitz operators via Mourre conjugate operators.

Findings

Proves the limiting absorption principle for the class of operators.

Shows absence of singular continuous spectrum.

Establishes existence and completeness of wave operators.

Abstract

We analyse spectral properties of a class of compact perturbations of block Toeplitz operators associated with analytic symbols. In particular, a limiting absorption principle and the absence of singular continuous spectrum are shown. The existence and the completeness of wave operators are also obtained. Our study is based on the construction of a conjugate operator in Mourre sense for the corresponding Laurent operators.