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

Beatriz Abadie·Ken Dykema
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Abstract

A notion of unique ergodicity relative to the fixed-point subalgebra 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 autormorphisms 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.

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Beatriz Abadie, Ken Dykema. 2006-08-16. Unique ergodicity of free shifts and some other automorphisms of C*-algebras. https://arxiv.org/abs/math/0608227

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