Journal of Operator Theory

Volume 61, Issue 2, Spring 2009 pp. 279-294.

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

Authors: Beatriz Abadie (1) and Ken Dykema (2)
Author institution: (1) Centro de Matematicas, Facultad de Ciencias, Igua 4225, Montevideo, CP 11 400, Uruguay (2) Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA

Summary: A notion of unique ergodicity relative to the fixed-point subalgebra is defined for automorphisms of unital \cstar-algebras. It is proved that the free shift on any reduced amalgamated free product \cstar-algebra is uniquely ergodic relative to its fixed-point subalgebra, as are automorphisms of reduced group \cstar-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 \cstar-algebras, is proved.

Keywords: Unique ergodicity, ergodic averages, free shift, Haagerup inequality, property (RD)

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