Cosine families of operators in a class of Fréchet spaces

  • Rachid Ameziane Hassani Université Sidi Mohamed Ben Abdellah.
  • Aziz Blali Université Sidi Mohamed Ben Abdellah.
  • Abdelkhalek El Amrani Université Sidi Mohamed Ben Abdellah.
  • Khalil Moussaouja Université Sidi Mohamed Ben Abdellah.
Palabras clave: Strongly continuous cosine families, Semi-groups of operators, Locally convex space, Quojection Fréchet space.

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.

Biografía del autor

Rachid Ameziane Hassani, Université Sidi Mohamed Ben Abdellah.
Faculté des Sciences Dhar-Mehraz, Departement de Mathematiques.
Aziz Blali, Université Sidi Mohamed Ben Abdellah.
Faculté des Sciences Dhar-Mehraz, Departement de Mathematiques.
Abdelkhalek El Amrani, Université Sidi Mohamed Ben Abdellah.
Faculté des Sciences Dhar-Mehraz, Departement de Mathematiques.
Khalil Moussaouja, Université Sidi Mohamed Ben Abdellah.
Faculté des Sciences Dhar-Mehraz, Departement de Mathematiques.

Citas

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[7] Meise, R., Vogt, D, introduction to Function Analysis, pp.326-356, Clarendon press, Oxford, (1997)

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[9] Serge L., Real and Functional Analysis, pp.396. third ed., Grad. Texts in Math., Vol. 142, Springer-Verlag, NewYork, (1993)

[10] Sova, M,. Cosine operator functions. Rozprawy Mat. 49, pp. 1-47, (1966)
Publicado
2018-03-15
Cómo citar
Hassani, R., Blali, A., El Amrani, A., & Moussaouja, K. (2018). Cosine families of operators in a class of Fréchet spaces. Proyecciones. Journal of Mathematics, 37(1), 103-118. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2783
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