Cosine families of operators in a class of Fréchet spaces

Rachid Ameziane Hassani, Aziz Blali, Abdelkhalek El Amrani, Khalil Moussaouja


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.

Palabras clave

Strongly continuous cosine families; Semi-groups of operators; Locally convex space; Quojection Fréchet space.

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