Complete wave operators in non-selfadjoint Kato model of smooth perturbation theory

Subject of the paper deals with the perturbation theory of linear operators acting in Hilbert space. For a certain class of perturbations the question is considered about existence of transformation operators implementing linear similarity of perturbed and unperturbed operators. In this context some results of complex analysis prove to be useful as well as the relationship with the theory of operator semi-groups.