Unique ergodicity of free shifts and some other automorphisms of C* -algebras

A notion of unique ergodicity relative to the fixed-point subalge- bra is defined for automorphisms of unital C* -algebras. It is proved that the free shift on any reduced amalgamated free product C* -algebra is uniquely ergodic relative to its fixed-point subalgebra, as are automorphisms of reduced group C* -algebras arising from certain automorphisms of groups. A generalization of Haagerup's inequality, yielding bounds on the norms of certain elements in reduced amalgamated free product C* -algebras, is proved. Copyright by THETA, 2009.

Unique ergodicity of free shifts and some other automorphisms of C* -algebras Academic Article