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Dynamical semigroups commuting with compact abelian actions

Published online by Cambridge University Press:  19 September 2008

Ola Bratteli  and
David E. Evans
Ola Bratteli
Affiliation:
Institute of Mathematics, University of Trondheim, 7034 Trondheim – NTH, Norway
David E. Evans
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CVA 7AL, England
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Abstract

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Let be a C*-algebra and τ:G → Aut a compact abelian action such that the fixed point algebra τ is simple. Denote by F the *-subalgebra of G-finite elements. Let H: F → be a *-operator commuting with τ such that and the matrix inequality

holds for all finite sequences X1, …, Xn in F. Then H is closable, and the closure is the generator of a strongly continuous semigroup {exp (−t): t ≥ 0} of completely positive contractions. Furthermore, there exists a convolution semigroup {μt: t ≥ 0} of probability measures on G such that

.

This result has various extensions and refinements.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 2 , June 1983 , pp. 187 - 217
Copyright
Copyright © Cambridge University Press 1983

References

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