Ergodicity of commuting multioperators and holomorphic multioperators of multiplication

Abstract

In this paper, the strong ergodic theorems are extended from the case of one bounded operator to the case of commuting multioperators. The authors show that in Grothendieck space with the Dunford-Pettis property, mean ergodic operator, and uniform ergodic operator are the same. We study when multioperators of multiplication on a weighted Banach space of holomorphic multi-functions are power bounded, mean ergodic, or uniformly mean ergodic.