Zeitschrift für Analysis und ihre Anwendungen
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On Conditional Expectations Arising from Group ActionsMichael Frank, V.M. Manuilov and E.V. Troitsky (1) Mathematisches Institut, Hochschule für Technik, Wirtschaft und Kultur, PF 301166, 04251, LEIPZIG, GERMANY
(2) Department of Mathematics, Moscow State University, 119899, MOSCOW, RUSSIAN FEDERATION
(3) Department of Mathematics, Moscow State University, 119899, MOSCOW, 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