Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: alg-geom