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Cosine families of operators in a class of Fréchet spaces
2018
Proyecciones
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. Keywords : Strongly continuous cosine families. Semi-groups of operators.
doi:10.4067/s0716-09172018000100103
fatcat:5ijvkdesr5aenplzli5er2nm4e