This article is cited in 4 papers

Brief communications

On Strictly Weakly Mixing $C^*$-Dynamical Systems

F. M. Mukhamedov

National University of Uzbekistan named after M. Ulugbek

Abstract: We consider strictly ergodic and strictly weakly mixing $C^*$-dynamical systems. We establish that a system is strictly weakly mixing if and only if its tensor product is strictly ergodic and strictly weakly mixing. We also investigate some weighted uniform ergodic theorem with respect to $S$-Besicovitch sequences for strictly weakly mixing dynamical systems.

Keywords: strict ergodicity, strictly weak mixing, $C^*$-dynamical system, $S$-Besicovitch sequence.

UDC: 517.98

Received: 29.10.2005

DOI: 10.4213/faa2883

 English version: Functional Analysis and Its Applications, 2007, 41:4, 311–313

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