Cosine families of operators in a class of Fréchet spaces.
Author
Hassani, Rachid Ameziane
Blali, Aziz
El Amrani, Abdelkhalek
Moussaouja, Khalil
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 Fréchet spaces, and we prove that the infinitesimal generator of an uniformly continuous cosine family of operators in a class of Fréchet spaces (quojection) is necessarily continuous.