On a class of operators in the hyperfinite ${\rm II}_1$ factor
| Autor: | Zhu, Zhangsheng, Fang, Junsheng, Shi, Rui |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $R$ be the hyperfinite ${\rm II}_1$ 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. Comment: 20pages. arXiv admin note: text overlap with arXiv:0708.1968 by other authors |
| Databáze: | arXiv |
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