Perturbations of generators of C0-semigroups and resolvent decay

Authors:

• Charles J.K. Batty,
• Sebastian Mariusz Król

Abstract

We obtain new stability results for those properties of C₀-semigroups which admit characterisation in terms of decay of resolvents of infinitesimal generators on vertical lines, e.g. analyticity, Crandall-Pazy differentiability or immediate norm continuity in the case of Hilbert spaces. As a consequence we get a generalisation of the Kato-Neuberger theorem on approximation of the identity. Finally, we present examples shedding a new light on resolvent characterisation of eventually differentiable C₀-semigroups for which differentiability is stable under bounded perturbations. © 2010 Elsevier Inc. All rights reserved.