  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".
