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Let λ denote the left regular representation of a locally compact group G on L 2 (G) and C*(λ(G)) the C*-algebra generated by λ(G). We show that the amenability of G and the amenability of G considered as a discrete group both may be characterized in terms of C*(λ(G))

On the 𝐶*-algebra generated by the left regular representation of a locally compact group