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Bergelson's theorem for weakly mixing C*-dynamical systems

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Duvenhage R.

Studia Mathematica

2009

tom 192

nr 3

235-257

We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khinchin's recurrence theorem obtained by Bergelson in the measure-theoretic case. A noncommutative recurrence theorem for such systems is obtained as a corollary.

Relatively independent joinings and subsystems of W*-dynamical systems

100%

Duvenhage R.

Studia Mathematica

2012

tom 209

nr 1

21-41

Relatively independent joinings of W*-dynamical systems are constructed. This is intimately related to subsystems of W*-dynamical systems, and therefore we also study general properties of subsystems, in particular fixed point subsystems and compact subsystems. This allows us to obtain characterizations of weak mixing and relative ergodicity, as well as of certain compact subsystems, in terms of joinings.

Ograniczanie wyników

2 Studia Mathematica

2 Duvenhage R.

1 2012

1 2009

Wyniki wyszukiwania

Bergelson's theorem for weakly mixing C*-dynamical systems

Relatively independent joinings and subsystems of W*-dynamical systems