Spectral theory for perturbed block Toeplitz operators
We propose to discuss spectral properties, mainly important for scattering theory, of certain perturbed Toeplitz operators. Problems are treated for the general case, in an abstract framework, using direct methods of perturbation theory. Applications to block Jacobi matrices and also to perturbed periodic Jacobi matrices will be considered. In particular, estimates for the number of the eigenvalues created by perturbations in the spectral gaps will be also presented.