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

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.

arXiv commentThe revision (2006/08/16) includes a comment that our generalization of Haagerup's inequality can, in fact, be obtained from Ricard+Xu's results, and some other minor changes

References in corpus (1)

• Strict weak mixing of some C*-dynamical systems based on free shifts

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