On the admissibility of observation for perturbed C0C0-semigroups on Banach spaces

This paper concerns linear infinite-dimensional systems with unbounded observation operators. We study the invariance of admissibility for observation operators under some unbounded perturbations of the generator. We give also some relations between the ΛΛ-extensions of such observation operators with respect to the original generator and the perturbed generator. Our results are applied to functional differential linear systems.