On a class of operators in the hyperfinite ${\mathrm{II}}_1$ factor

Zhangsheng Zhu, Junsheng Fang, Rui Shi

Let $R$ be the hyperfinite ${\mathrm{II}}_1$ factor and let $u,v$ be two generators of $R$ such that $u^{\ast }u=v^{\ast }v=1$ and $vu=e^{2\pi i\theta }uv$ for an irrational number $\theta$. In this paper we st…