On the growth of semigroups and perturbations

Abstract

In this work, we investigate types of boundedness of a semigroup on a Banach space in terms of the Cesaro-average and the behavior of the resolvent at the origin. We establish a characterization of type Hille–Yosida for the generators of \(\varphi \)-bounded strongly continuous semigroups. Moreover, these results are used to study the effect of the perturbation on the type of the growth.