Uniform Exponential Stability of Perturbed Semigroups: The Dyson–Phillips Formula Versus Gil’s Approach Via Commutators

Abstract We discuss the uniform exponential stability of strongly continuous semigroups generated by operators form $$ A+B A + B , where B is a bounded perturbation generator A . compare two approaches to problem: via Dyson–Phillips formula and size norm commutator - method recently developed M. Gil’. show that quite often first approach more powerful than second one and, importantly, easier use.