On ergodic type theorems for strictly weak mixing C^*-dynamical systems
Abstract
Description
We prove that unique ergodicity of tensor product of $C^*$-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
12 pages