International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 5, Pages 307-319
-continuity of the Fröbenius-Perron semigroup
1Mathématiques Pures et Appliquées (UMPA) UMR 5669 CNRS-ENS Lyon Directeur, 46, gone from Italy, LYON Cedex 07 69364, France
2Departamento de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Received 22 May 2001
Copyright © 2002 Andrés Navas and Sergio Plaza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space endowed with a finite or a -finite regular measure. We prove that if there exists a faithful invariant measure for the semidynamical system, then the Fröbenius-Perron semigroup of linear operators is -continuous in the space . We also give a geometrical condition which ensures -continuity of the Fröbenius-Perron semigroup of linear operators in the space for , as well as in the space