ERGODIC AMENABLE ACTIONS OF ALGEBRAIC GROUPS

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 theory of amenable semigroup actions

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

Amenable Actions of Nonamenable Groups

Since 1929 when von Neumann [vN29] introduced the notion of an invariant mean on a group (and more generally on a G-set) there is a permanent interest in the study of the phenomenon known as amenability. Amenable objects like groups, semigroups, algebras, graphs, metric spaces, operator algebras etc. play an important role in different areas of mathematics. A big progress in understanding of th...

Orbit Inequivalent Actions of Non-amenable Groups

This is a preliminary note containing the proof that every countable non-amenable group admits continuum many orbit inequivalent free, measure preserving, ergodic actions on a standard Borel space with probability measure. 1. Summary and Notation Let Γ1 y α1 (X1, μ1),Γ2 y α2 (X2, μ2) be Borel measure preserving actions. α1 and α2 are orbit equivalent if there exist conull subsets A1 ⊂ X1, A2 ⊂ ...