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Zeitschrift für Analysis und ihre Anwendungen

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Volume 16, Issue 4, 1997, pp. 831–850
DOI: 10.4171/ZAA/794

Published online: 1997-12-31

On Conditional Expectations Arising from Group Actions

Michael Frank[1], V.M. Manuilov[2] and E.V. Troitsky[3]

(1) Hochschule für Technik, Wirtschaft und Kultur, Leipzig, Germany
(2) Moscow State University, Russian Federation
(3) Moscow State University, Russian Federation

Induced conditional expectations of finite index on crossed product $C*$-algebras are considered which are non-algebraically of finite index. The characteristics of actions of (amenable) topological groups on compact Hausdorff spaces $X$ are investigated, ensuring the appearance of a well-defined induced conditional expectation on the corresponding commutative $C*$-a1gebra $C(X)$ and its property to be of finite index. For this purpose Hilbert $C*$-module and topological techniques are used. Special emphasis is placed on discrete group actions.

Keywords: Group actions on compact spaces, induced conditional expectations of finite index, crossed product $C*$-algebras, commutative $C*$-a1gebras

Frank Michael, Manuilov V.M., Troitsky E.V.: On Conditional Expectations Arising from Group Actions. Z. Anal. Anwend. 16 (1997), 831-850. doi: 10.4171/ZAA/794