Spectral theory for structured perturbations of linear operators

Abstract

We characterize the spectrum (and its parts) of operators which can be represented as "$G=A+BC“$ for a "simpler" operator $A$ and a structured perturbation $BC$. The interest in this kind of perturbations is motivated, e.g., by perturbations of the domain of an operator $A$ but also arises in the theory of closed-loop systems in control theory. In many cases our results yield the spectral values of $G$ as zeros of a "characteristic equation".