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Please tell me where can I see the proof of this well-known fact? enter image description here

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  • $\begingroup$ Not sure where to find the proof. But by universality of your universal $C^{\ast}$-algerba there exists a homomorphism of $C^{\ast}(G,R)\to \mathcal T$, where $\mathcal T$ is the Toeplitz algebra, since $\mathcal T$ has a single generator this homorphism is surjective , injectivity of the homomorphism requires a bit more work but is somewhat easy to see. $\endgroup$
    – esteban
    Feb 10, 2023 at 14:31
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    $\begingroup$ You should find this in Murphy's book on "C*-algebras and operator theory" $\endgroup$
    – Botwinnik
    Feb 10, 2023 at 14:56

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