Asymptotic properties of $C_0$-semigroups under perturbations

Abstract

For a given $C_0$-semigroup $(T(t){)}_{t\ge 0}$ we consider Staffans-Weiss perturbations $(B,C)$ of its generator as studied in [1] and investigate the robustness of asymptotic properties of the perturbed $C_0$-semigroup $(T_{BC}(t){)}_{t\ge 0}$. As a concrete application we study the asymptotic behavior of a neutral semigroup.