On a class of operators in the hyperfinite II1 factor

• Zhangsheng Zhu ^[1] ; Junsheng Fang ^[1] ; Rui Shi ^[1]
  1. [1] Dalian University of Technology-CHINA
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 2, 2017, págs. 249-271
• Idioma: inglés
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• Resumen

  • 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=e2πiθuv 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 S1. 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.