Compact actions commuting with ergodic actions and applications to crossed products

Peligrad, C.

doi:10.1090/S0002-9947-1992-1044964-4

Compact actions commuting with ergodic actions and applications to crossed products
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Trans. Amer. Math. Soc. 331 (1992), 825-836 Request permission

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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