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

TL;DR

This paper investigates the existence of transformation operators that establish linear similarity between perturbed and unperturbed operators within a specific class of non-selfadjoint perturbations, utilizing complex analysis and operator semi-group theory.

Contribution

It provides new results on the existence of wave operators in the non-selfadjoint Kato model of smooth perturbation theory, expanding understanding of operator similarity in this context.

Findings

Established conditions for the existence of wave operators

Linked complex analysis techniques with operator semi-group theory

Extended the theory of linear similarity in non-selfadjoint perturbations

Abstract

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.