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

Albanese, A. A., Bonet, J. Ricker, W. J., Grothendieck spaces with the DunfordPettis property, Positivity, 14, pp. 145-164, (2010).

Arendt, W., Batty, C. J. K., Hieber, M., Neubrander, F.: VectorValued Laplace Transforms and Cauchy Problems, Birkhauser, Basel, pp. 202-210, (2001)

Dierolf, S., Zarnadze, D. N., A note on strictly regular Fréchet spaces, Arch. Math., 42, pp. 549-556, (1984).

Dieter L., Strongly continuous operator cosine functions, Functional analysis (Dubrovnik, 1981) Lecture Notes in Math., vol. 948, Springer, Berlin-New York, pp. 73-97 (1982)

Fattorini, H. O.: Ordinary differential equations in linear topological spaces, II. J. Differential Equations 6, pp. 24-34, (1969)

Jarchow, H., locally Convex Space, pp. 156, B. G. Teubner, stuttgart, (1981)

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

Schaefer, H. H, Topological Vector Spaces, pp. 101. Graduate textes in MAthematics, springer-verlag, Berlin Heidelberg New York, (1971)

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

Sova, M,. Cosine operator functions. Rozprawy Mat. 49, pp. 1-47, (1966)

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.

Issue

Section

Artículos

Most read articles by the same author(s)

1 2 > >>