Non-commutative ergodic Theorems for actions of the hyperbolic groups

TL;DR

This paper establishes non-commutative pointwise ergodic theorems for actions of hyperbolic groups, expanding on prior work by other researchers in the field.

Contribution

It extends non-commutative ergodic theorems specifically to hyperbolic group actions, building on previous results and clarifying their applicability.

Findings

Proves non-commutative pointwise ergodic theorems for hyperbolic groups

Builds on and expands previous results by Bufetov, Khristoforov, Klimenko, Pollicott, and Sharp

Provides a framework for future research in non-commutative ergodic theory

Abstract

The goal of this notice is to establish Not-commutative Point- wise Ergodic Theorems for actions of the Hyperbolic Groups. Similar non-commutative results were done by Bufetov, Khristoforov and Kli- menko, and later by Pollicott and Sharp. We were interested to expand short notice in Policott and Sharp's paper about non-commutative er- godic theorems.