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

Francesco Fidaleo; Farrukh Mukhamedov

doi:10.1016/j.jmaa.2007.02.066

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

Francesco Fidaleo, Farrukh Mukhamedov

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

We define a stronger property than unique ergodicity with respect to the fixed-point subalgebra firstly investigated in [B. Abadie, K. Dykema, Unique ergodicity of free shifts and some other automorphisms of C^*-algebras, math.OA/0608227]. Such a property is denoted as F-strict weak mixing (F stands for the unital completely positive projection onto the fixed-point operator system). Then we show that the free shifts on the reduced C^*-algebras of RD-groups, including the free group on infinitely many generators, and amalgamated free product C^*-algebras, considered in [B. Abadie, K. Dykema, Unique ergodicity of free shifts and some other automorphisms of C^*-algebras, math.OA/0608227], are all strictly weak mixing and not only uniquely ergodic.

Original language	English
Pages (from-to)	180-187
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	336
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2007.02.066
Publication status	Published - Dec 1 2007
Externally published	Yes

Keywords

C-dynamical systems
Ergodic theory
Free products with amalgamation

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2007.02.066

Cite this

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title = "Strict weak mixing of some C*-dynamical systems based on free shifts",

abstract = "We define a stronger property than unique ergodicity with respect to the fixed-point subalgebra firstly investigated in [B. Abadie, K. Dykema, Unique ergodicity of free shifts and some other automorphisms of C*-algebras, math.OA/0608227]. Such a property is denoted as F-strict weak mixing (F stands for the unital completely positive projection onto the fixed-point operator system). Then we show that the free shifts on the reduced C*-algebras of RD-groups, including the free group on infinitely many generators, and amalgamated free product C*-algebras, considered in [B. Abadie, K. Dykema, Unique ergodicity of free shifts and some other automorphisms of C*-algebras, math.OA/0608227], are all strictly weak mixing and not only uniquely ergodic.",

keywords = "C-dynamical systems, Ergodic theory, Free products with amalgamation",

author = "Francesco Fidaleo and Farrukh Mukhamedov",

note = "Funding Information: The second-named author (F.M.) thanks FCT (Portugal) grant SFRH/BPD/17419/2004, and Professor L. Accardi for kind hospitality from 18–22 June 2006 at “Universit{\`a} di Roma Tor Vergata”. The authors are also grateful to the referee for useful suggestions.",

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AU - Mukhamedov, Farrukh

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