  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.
