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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Compact actions commuting with ergodic actions and applications to crossed products


Author: C. Peligrad
Journal: Trans. Amer. Math. Soc. 331 (1992), 825-836
MSC: Primary 46L55; Secondary 22D25
MathSciNet review: 1044964
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Abstract: Let $ (A,K,\beta)$ be a $ {C^{\ast}}$-dynamical system with $ K$ compact. In this paper we prove a duality result for saturated actions (Theorem 3.3). The proof of this result can also be considered as an alternate proof of the corresponding result for von Neumann algebras due to Araki, Haag, Kastler and Takesaki $ [14]$. We also obtain results concerning the simplicity and the primeness of the crossed product $ A \times _\beta K$ in terms of the ergodicity of the commutant of $ \beta $ (Propositions 5.3 and 5.4).


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1044964-4
PII: S 0002-9947(1992)1044964-4
Article copyright: © Copyright 1992 American Mathematical Society