Uniformly ergodic theorem for commuting multioperators

Abstract

In this paper, we established some uniformly Ergodic theorems by using multioperators satisfying the E-k condition introduce in [3]. One consequence, is that if $I-T$ is quasi-Fredholm and satisfies E-k condition then $T$ is uniformly ergodic. Also we give some conditions for uniform ergodicity of a commuting multioperators satisfies condition E-k. These results are of interest in view of analogous results for unvalued operators (see, for example [2]) also in view of the recent developments in the ergodic theory and its applications.

Keywords

• Average
• E-k condition
• finite descent
• uniform ergodicity.