Hereditary $C^*$-subalgebras of $C^*$-crossed products
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- by Masaharu Kusuda PDF
- Proc. Amer. Math. Soc. 102 (1988), 90-94 Request permission
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
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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