Formula of the regularized trace for perturbation in the Schatten - von Neumann of discrete operators

Abstract

Abstract.In the paper we study a regularized trace formula for discrete self-adjoint operators with a perturbation in Schatten-von Neumann class ( , ∈ N). We prove that the regularized trace vanishes after deducting ( − 1) terms of perturbation theory if there are no dilating gaps in the spectrum of the unperturbed operator.