Indexed by:期刊论文
Date of Publication:2017-01-01
Journal:Mathematica Scandinavica
Included Journals:SCIE
Volume:120
Issue:2
Page Number:249-271
ISSN No.:0025-5521
Abstract:Let R be the hyperfinite II1 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 of (v) and the identity operator is a generalized universal irrational rotation C*-algebra.