Cosine families of operators in a class of Fréchet spaces.

• Autores: Rachid Ameziane Hassani, Aziz Blali, Abdelkhalek El Amrani, Khalil Moussaouja
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 37, Nº. 1, 2018, págs. 103-118
• Idioma: inglés
• DOI: 10.4067/s0716-09172018000100103
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• Resumen

  • 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.

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