## Infinite number of non-isomorphic von Neumann algebras with property Gamma?

A II$_1$ factor $\mathcal M$ with trace $\tau$ has property Gamma if for every $\epsilon > 0$ and finite set $\{x_1,\cdots, x_n\} \subset \mathcal M$ there exists a trace 0 unitary element $y\in\mathcal M$ such that $\sum_{i=1}^n \|x_iy – yx_i\|_2 < \epsilon$, where the 2-norm is $\|a\|_2 = \tau(a^*a)^{1/2}$. Murray and von Neumann defined this … Read more