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

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 Dot only uniquely ergodic. (c) 2007 Elsevier Inc. All rights reserved