English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Let $R$ be the hyperfinite ${\rm II}_1$ factor and let $u,v$ be twogenerators of $R$ such that $u^*u=v^*v=1$ and $vu=e^{2\pi i\theta} uv$ for anirrational 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 $uf(v)$, andstudy the invariant subspace problem of such operators relative to $R$. We showthat under general assumptions the von Neumann algebra generated by $uf(v)$ isan irreducible subfactor of $R$ with index $n$ for some natural number $n$, andthe $C^*$-algebra generated by $uf(v)$ and the identity operator is ageneralized universal irrational rotation $C^*$-algebra.

On a class of operators in the hyperfinite ${\rm II}_1$ factor