Über Die Konvergenz Operatorwertiger Cosinusfunktionen mit Gestörtem Infinitesimalen Erzeuger

On convergence of operator cosine functions with perturbed infinitesimal generator. The question under what kind of perturbations a closed linear operatorA remains of the class of infinitesimal generators of operator cosine functions seems to be a rather difficult one and is unsolved in general. In this note we give bounds for the perturbation of operator cosine functions caused byA-bounded perturbationsT ofA under the assumption thatT + A is also a generator.