International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 5, Pages 307-319
doi:10.1155/S0161171202013364
C0-continuity of the Fröbenius-Perron semigroup
Andrés Navas1
and Sergio Plaza2
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
Abstract
We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ-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 C0-continuous in the space Lμ 1(X). We also give a geometrical condition which ensures C0-continuity of the Fröbenius-Perron semigroup of linear operators in the space Lμ p(X) for 1≤p<∞, as well as in the space Lloc 1 .