@article{Zhu_Fang_Shi_2017, title={On a class of operators in the hyperfinite $\mathrm{II}_1$ factor}, volume={120}, url={https://www.mscand.dk/article/view/25625}, DOI={10.7146/math.scand.a-25625}, abstractNote={<p>Let $R$ be the hyperfinite $\mathrm {II}_1$ factor and let $u$, $v$ be two generators of $R$ such that $u^*u=v^*v=1$ and $vu=e^{2\pi i\theta } uv$ for an irrational number $\theta$. In this paper we study the class of operators $uf(v)$, where $f$ is a bounded Lebesgue measurable function on the unit circle $S^1$. We calculate the spectrum and Brown spectrum of operators $uf(v)$, and study the invariant subspace problem of such operators relative to $R$. We show that under general assumptions the von Neumann algebra generated by $uf(v)$ is an irreducible subfactor of $R$ with index $n$ for some natural number $n$, and the $C^*$-algebra generated by $uf(v)$ and the identity operator is a generalized universal irrational rotation $C^*$-algebra.</p>}, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Zhu, Zhangsheng and Fang, Junsheng and Shi, Rui}, year={2017}, month={May}, pages={249–271} }