IJPAM: Volume 23, No. 2 (2005)

UNIFORMLY ERGODIC THEOREM FOR SEMIGROUPS
WITH $k$-DECOMPOSABLE KATO
INFINITESIMAL GENERATORS

S. Lahrech$^1$, A. Azizi$^2$, A. Ghomari$^3$, A. Mbarki$^4$, A. Ouahab$^5$
$^{1,2,3,4,5}$Department of Mathematics
Faculty of Science
Mohamed First University
Oujda, MOROCCO
$^1$e-mail: lahrech@sciences.univ-oujda.ac.ma
$^2$e-mail: azizi@sciences.univ-oujda.ac.ma
$^3$e-mail: ghomari@sciences.univ-oujda.ac.ma
$^4$e-mail: mbarki@sciences.univ-oujda.ac.ma
$^5$e-mail: ouahab@sciences.univ-oujda.ac.ma


Abstract.In this paper we shall extend the technical assumption $(E-k)$ to semigroups. We prove that if $T=(T(t), t\geq 0)$ is $C_0$-semigroup of operators in $L(X)$ with $k$-decomposable Kato infinitesimal generator $A$ satisfying the condition $(E-k)$, then $T$ is uniformly ergodic. These results are of interest in view of recent activity in the ergodic theory and its applications.

Received: June 13, 2005

AMS Subject Classification: 47A35, 47A13

Key Words and Phrases: average, semigroups, $(E-k)$ condition, uniform ergodicity, $k$-decomposable operators, Kato operators

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 23
Issue: 2