IJPAM: Volume 23, No. 2 (2005)

UNIFORMLY ERGODIC THEOREM AND FINITE
CHAIN LENGTH FOR MULTIOPERATORS

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.The main purpose of this paper is to extend the technical assumption $(E-k)$ of [#!r2!#] to multioperators. We give necessary and sufficient conditions for uniform ergodicity of a commuting multioperator satisfying the condition $(E-k).$ Those results are of interest in view of analogous results for valued operators established in [#!r2!#] and in view of recent activity in the ergodic theory and its applications (see, for example [#!r3!#]).

Received: June 13, 2005

AMS Subject Classification: 47A35, 47A13

Key Words and Phrases: average, $(E-k)$ condition, finite descent, uniform ergodicity

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