Zeitschrift für Analysis und ihre Anwendungen


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

On Conditional Expectations Arising from Group Actions

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

(1) Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109, 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 M, Manuilov V, Troitsky E. On Conditional Expectations Arising from Group Actions. Z. Anal. Anwend. 16 (1997), 831-850. doi: 10.4171/ZAA/794