arXiv subjects

Anton Stroh

Publications and source records attributed to Anton Stroh.

6 recordsLinked to original sources

arXiv2011

Disjointness and unique ergodicity of C*-dynamical systems

We study an ergodic theorem for disjoint C*-dynamical systems, where disjointness here is a noncommutative version of the concept introduced by Furstenberg for classical dynamical systems. This is applied to W*-dynamical systems. We also consider specific examples of disjoint C*-dynamical and W*-dynamical systems, including for actions of other groups than $\mathbb{Z}$. Unique ergodicity and unique ergodicity relative to the fixed point algebra are closely related to disjointness, and are used to give examples of disjoint C*-dynamical systems.

math.OA↗

arXiv2010

The Szemeredi property in ergodic W*-dynamical systems

We study weak mixing of all orders for asymptotically abelian weakly mixing state preserving C*-dynamical systems, where the dynamics is given by the action of an abelian second countable locally compact group which contains a Folner sequence satisfying the Tempelman condition. For a smaller class of groups (which include Z^q and R^q) this is then used to show that an asymptotically abelian ergodic W*-dynamical system either has the "Szemeredi property" or contains a nontrivial subsystem (a "compact factor") that does. A van der Corput lemma for Hilbert space valued functions on the group is one of our main technical tools.

math.OA↗

arXiv2006

The Szemeredi property for compact C*-dynamical systems

Furstenberg's multiple recurrence result for measure theoretic dynamical systems is proved for compact C*-dynamical systems for which the evolution is given by a semigroup with the right cancellation property, a right invariant measure and containing a Folner net.

math.OA↗

arXiv2005

A van der Corput lemma and weak mixing over groups

We study weak mixing of all orders for weakly mixing measure preserving dynamical systems, where the dynamics is given by the action of an abelian second countable topological group which has an invariant measure under the group operation. One of the main technical tools we use is a van der Corput lemma for Hilbert space valued functions on a second countable topological group.

math.DS↗

arXiv2005

Noncommutative recurrence over locally compact Hausdorff groups

We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a form of multiple recurrence. This is done using the mean ergodic theorem in Hilbert space, via the GNS construction.

math.DS↗

arXiv2002

Recurrence and ergodicity in unital *-algebras

Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried over to a non-commutative *-algebraic setting using the GNS-construction. This generalizes the corresponding measure theoretic results, in particular a variation of Khintchine's Theorem for ergodic systems, where the image of one set overlaps with another set, instead of with itself.

math.DS↗