2008/02/14 by Francesco Fidaleo, Fidaleo, Francesco · 1 citation
Mathematics · Physics and Astronomy · #20E06 #37A30 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.DS #math.OA #msc:20E06 #msc:37A30 #msc:46L55
paper · pdf · doi:10.48550/arxiv.0802.2076
13 pages. Infin. Dimens. Anal. Quantum Probab. Relat. Top., to appear
openalex publication_date 2008/02/14 · arxiv created 2009/08/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the the shift on the reduced C*--algebras of RD--groups, including the free group on infinitely many generators, and the amalgamated free product C*--algebras, enjoys the very strong ergodic property of the convergence to the equilibrium. Namely, the free shift converges, pointwise in the weak topology, to the conditional expectation onto the fixed--point subalgebra. Provided the invariant state is unique, we also show that such an ergodic property cannot be fulfilled by any classical dynamical system, unless it is conjugate to the trivial one--point dynamical system.