Regularized traces of discrete operators

Unbounded perturbations of discrete operators are considered. Formulas for regularized traces are obtained, in which a finite number of corrections of the perturbation theory are used. An exact relation is established between the degree of subordination of a perturbation to the unperturbed operator and the number of corrections necessary for the existence of a finite formula of the trace. New estimates for the kernel norm of a resolvent of discrete operators are obtained.