Discrete spectrum in the gaps for perturbations of periodic Jacobi matrices (Q1005999)

The paper considers a periodic Jacobi matrix \(A\) which is perturbed with a bounded operator. The author gives conditions under which the set of perturbed eigenvalues in each spectral gap of \(A\) is only finite. The results are obtained from the point of view of techniques of the perturbation theory of operators and revise and extend those obtained earlier by the same author. The methods developed in the present paper can be applied to more general operators, involving block Toeplitz operators or matrix Wiener--Hopf type operators.