Journal of Mathematical Sciences

, Volume 140, Issue 3, pp 398–425 | Cite as

Unitary representations and modular actions

  • A. S. Kechris


We call a measure-preserving action of a countable discrete group on a standard probability space tempered if the associated Koopman representation restricted to the orthogonal complement to the constant functions is weakly contained in the regular representation. Extending a result of Hjorth, we show that every tempered action is antimodular, i.e., in a precise sense “orthogonal” to any Borel action of a countable group by automorphisms on a countable rooted tree. We also study tempered actions of countable groups by automorphisms on compact metrizable groups, where it turns out that this notion has several ergodic theoretic reformulations and fits naturally in a hierarchy of strong ergodicity properties strictly between ergodicity and strong mixing. Bibliography:s 25 titles.


Invariant Measure Unitary Representation Cayley Graph Regular Representation Countable Group 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. S. Kechris
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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