This article is cited in 3 papers

On uniform ergodic theorems for quadratic processes on $C^*$-algebras

F. M. Mukhamedov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We investigate questions of the convergence in the uniform topology of Ceséaro 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 $\Phi$-functions converge.

UDC: 517.98+519.217

MSC: Primary 37A50; Secondary 46L53, 60G99

Received: 06.05.1998 and 25.01.1999

DOI: 10.4213/sm532

 English version: Sbornik: Mathematics, 2000, 191:12, 1891–1903

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