On uniform ergodic theorems for quadratic processes on <i>C*</i> -algebras
Farrukh MukhamedovRomanovskii Mathematical Institute of the National Academy of Sciences of the Uzbek Republic, Tashkent, Uzbekistan
ABI
Abstract
We investigate questions of the convergence in the uniform topology of Cesearo time averages of stationary quantum quadratic processes defined on C*-algebras.A necessary and sufficient condition is given for the convergence of averages in the uniform topology. In addition, the convergence of weighted averages in the uniform topology is investigated and it is proved that averages weighted by Besicovitch Φ-functions converge.