# Compact ergodic groups of automorphisms

### Abstract

It is shown that if $G$ is a compact ergodic group of $\ast$-automorphisms on a unital $C^\ast$-algebra $A$ then the unique $G$-invariant state is a trace. Hence if $A$ is a von Neumann algebra then it is finite and injective.

## Authors

Raphael J. Høegh-Krohn