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Hereditary $ C^*$-subalgebras of $ C^*$-crossed products


Author: Masaharu Kusuda
Journal: Proc. Amer. Math. Soc. 102 (1988), 90-94
MSC: Primary 46L55
DOI: https://doi.org/10.1090/S0002-9939-1988-0915722-8
MathSciNet review: 915722
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Abstract: Let $ (A,G,\alpha )$ be a $ {C^ * }$-dynamical system. Assume that $ B$ is an $ \alpha $-invariant $ {C^ * }$ - subalgebra of $ A$. Then we shall give a necessary and sufficient condition for $ B{ \times _\alpha }G$ to be a $ {C^ * }$-subalgebra of $ A{ \times _\alpha }G$, where $ B{ \times _\alpha }G$ (resp. $ A{ \times _\alpha }G$) denotes a $ {C^ * }$-crossed product of $ B$ (resp. $ A$) by a locally compact group $ G$. Moreover, we shall show that if $ B$ is an $ \alpha $-invariant hereditary $ {C^ * }$-subalgebra of $ A$, then $ B{ \times _\alpha }G$ is a hereditary $ {C^ * }$-subalgebra of $ A{ \times _\alpha }G$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0915722-8
Keywords: $ {C^ * }$-crossed product, hereditary $ {C^*}$-subalgebra, $ {C^*}$-dynamical system
Article copyright: © Copyright 1988 American Mathematical Society

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