The method of similar operators in the spectral analysis of infinite operator matrices

Method of similar operators is a useful tool for studying the spectral properties of various classes of perturbed differential operators. In this paper, we exhibit a modification of the method which applies for a large class of operators. In particular, the spectrum of the unperturbed operator is not assumed to have increasing lacunas, which is a typical assumption for Hill operators. The method is presented in terms of the operator matrices. It can be used, for example, for first order differential operators with an involution, Dirac operators.