2 problems

Let $\Gamma$ be a discrete group, let $L(\Gamma)$ be its group von Neumann algebra, and let $\tau$ be the standard trace on $L(\Gamma)$. For $A\in M_n(\mathbb{Z}[\Gamma])$, write ……

Let $\Gamma$ be a group generated by $g_{1},\dots,g_{n}$ and assume that $L(\Gamma)$ can be embedded into $R^{\omega}$. Let $V\subset\ell^{2}(\Gamma)^{n}$ be the subspace … Let…