The Szemeredi property in ergodic W*-dynamical systems

Details The Szemeredi property in ergodic W*-dynamical systems The Szemeredi property in ergodic W*-dynamical systems

2007-09-11

arxiv.org/abs/0709.1557v3

J. Operator Theory 64 (2010), 35-67

Mathematics

Operator Algebras

v1: 39 pages. Incorporates large portions of the unpublished preprints math/0512059 and math/0611309. v2: Several corrections

Scientific paper

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.

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