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A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b)* = b* a* and the C*-identity ‖a* a‖ = ‖a‖². Related tags: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].
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Is the reduced group $C^*$-algebra quasidiagonal
Let $G$ be an amenable group. I wonder whether it is true that the reduced group $C^*$-algebra $C_r^*(G)$ is quasidiagonal.
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Two isomorphic reduced group $C^*$-algebras
Suppose that $C^*_r(G)\cong C^*_r(H)$, can we conclude that $G\cong H$?