Cosine families of operators in a class of Fréchet spaces

Abstract

M. sova [10] proved that the infinitesimal generator of all uniformly continuous cosine family, of operators in Banach space, is a bounded operator. We show by counter-example that the result mentioned above is not true in general on Frechet spaces, and we prove that the infinitesimal generator of an uniformly continuous cosine family of operators in a class of Frechet spaces (quojection) is necessarily continuous.