Is there a locally compact group $G$ such that the canonical map from $C^{*}(G)$ to $C^{*}_{red} G$ is not isomorphism, hence $G$ is not amenable but these two $C^{*}$ algebras are isomorphic $C^{*}$ algebras via another morphism?
Can the full and reduced group $C^*$-algebras be "noncanonically" isomorphic?
Ali Taghavi
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