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 not only uniquely ergodic.