Definition 12.3.15 (Group Von Neumann Algebra).label Let $G$ be a group and
\begin{align*}\lam:G&\inj U(\el^{2}(G))\\ g&\mto\lam_{g}\end{align*}
then $\lam_{g}(\de_{t})=\de_{gt}$. The group von Neumann algebra of $G$ is $L(G)=\cl{Span(\lam(G))}$ under SOT.
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