On a class of operators in the hyperfinite II_1 factor - Zhu, Zhangsheng; Fang, Junsheng; Shi, Rui (MATHEMATICA SCANDINAVICA, 2017)
Let R be the hyperfinite II_1 factor and let u, v be two generators of R such that u^*u=v^*v=1 and vu=e^2π iθ uv for an irrational number θ. 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.