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Question in “Fell” missing hypothesis?

I'm reading and studying Fell and Doran's book: Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles Chapter 3 is devoted to Locally compact groups. Exercise 35 says, ...
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261 views

Left regular representation of $L^1(G)$ for a locally compact group $G$

Let $G$ be a locally compact group (not discrete) and let $L$ be the left regular representation of $A = L^1(G)$ on itself i.e. $L: A \to \mathcal{B}(A)$ where $L(f): A \to A$, $L(f)(g) = f*g$. I want ...