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Conditional expectations in $ C\sp{\ast} $-crossed products


Author: Shigeru Itoh
Journal: Trans. Amer. Math. Soc. 267 (1981), 661-667
MSC: Primary 46L55
DOI: https://doi.org/10.1090/S0002-9947-1981-0626496-0
MathSciNet review: 626496
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Abstract: Let $ (A,\,G,\,\alpha )$ be a $ {C^{\ast}}$-dynamical system. Let $ B$ be a $ {C^{\ast}}$-subalgebra of $ A$ and $ P$ be a conditional expectation of $ A$ onto $ B$ such that $ {\alpha _t}P = P{\alpha _t}$ for each $ t \in G$. Then it is proved that there exists a conditional expectation of $ {C^{\ast}}(G,\,A,\,\alpha )$ onto $ {C^{\ast}}(G,\,B,\,\alpha )$. In particular, if $ G$ is amenable and $ A$ is unital, then there always exists a conditional expectation of $ {C^{\ast}}(G,\,A,\,\alpha )$ onto $ {C^{\ast}}(G)$. Some related results are also obtained.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1981-0626496-0
Keywords: $ {C^{\ast}}$-algebra, crossed product, conditional expectation
Article copyright: © Copyright 1981 American Mathematical Society

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