Cosine families of operators in a class of Fréchet spaces.

Authors

  • 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.

Keywords:

Strongly continuous cosine families, emi-groups of operators, Locally convex spac, Quojection Fréchet space

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.

Author Biographies

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.

References

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Published

2018-03-15

How to Cite

[1]
R. A. Hassani, A. Blali, A. El Amrani, and K. Moussaouja, “Cosine families of operators in a class of Fréchet spaces.”, Proyecciones (Antofagasta, On line), vol. 37, no. 1, pp. 103-118, Mar. 2018.

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