Ergodic theory of amenable semigroup actions

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.

Amenable Ergodic Actions , Hyperfinite Factors , and Poincaré Flows

1. Introduction. In this paper we announce the introduction of a new notion of amenability for ergodic group actions and ergodic equivalence relations. Amenable ergodic actions occupy a position in ergodic theory parallel to that of amenable groups in group theory and one can therefore expect this notion to be useful in diverse circumstances. Here we announce applications to hyperfinite factor ...

Ergodic Theorems on Amenable Groups

Ergodic Theorems on Amenable Groups

In 1931, Birkhoff gave a general and rigorous description of the ergodic hypothesis from statistical meachanics. This concept can be generalized by group actions of a large class of amenable groups on σ-finite measure spaces. The expansion of this theory culminated in Lindenstrauss’ celebrated proof of the general pointwise ergodic theorem in 2001. The talk is devoted to the introduction of abs...

Ergodic Theoretic Characterization of Left Amenable Lau Algebras