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Ergodic Actions of Compact Groups on Operator Algebras II: Classification of Full Multiplicity Ergodic Actions

Published online by Cambridge University Press:  20 November 2018

Antony Wassermann
Antony Wassermann*
Affiliation:
University of Liverpool,Liverpool, England
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In the first paper of this series [17], we set up some general machinery for studying ergodic actions of compact groups on von Neumann algebras, namely, those actions for which . In particular we obtained a characterisation of the full multiplicity ergodic actions:

THEOREM A. If α is an ergodic action of G on , then the following conditions are equivalent:

  • (1) Each spectral subspace has multiplicity dim π for π in .

  • (2) Each π in admits a unitary eigenmatrix in .

  • (3) The W* crossed product is a (Type I) factor.

  • (4) The C* crossed product of the C* algebra of norm continuity is isomorphic to the algebra of compact operators on a Hilbert space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 6 , 01 December 1988 , pp. 1482 - 1527
Copyright
Copyright © Canadian Mathematical Society 1988

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