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