Dynamical semigroups commuting with compact abelian actions
Open Access
- 1 June 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 3 (2) , 187-217
- https://doi.org/10.1017/s0143385700001929
Abstract
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.Keywords
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