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

2006/08/09 by Abadie, Beatriz, Dykema, Ken · 1 citation
#46L54 #46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0608227

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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• On universal property of reciprocal Kirchberg algebras and uniquely ergodic automorphisms

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