On ergodic type theorems for strictly weak mixing C^*-dynamical systems

Abstract

We prove that unique ergodicity of tensor product of $C^{\ast }$-dynamical system implies its strictly weak mixing. By means of this result a uniform weighted ergodic theorem with respect to $S$-Besicovitch sequences for strictly weak mixing dynamical systems is proved. Moreover, we provide certain examples of strictly weak mixing dynamical systems.

12 pages

References in corpus (2)

• Unique ergodicity of free shifts and some other automorphisms of C*-algebras
• Strict weak mixing of some C*-dynamical systems based on free shifts

Cited by in corpus (1)

• Free joinings of C*-dynamical systems