Similarity degree of a class of C${}^{\ast }$-algebras

Abstract

Suppose that $\mathcal{M}$ is a countably decomposable type II${}_1$ von Neumann algebra and $\mathcal{A}$ is a separable, non-nuclear, unital C${}^{\ast }$-algebra. We show that, if $\mathcal{M}$ has Property $\Gamma$, then the similarity degree of $\mathcal{M}$ is less than or equal to $5$. If $\mathcal{A}$ has Property c${}^{\ast }$-$\Gamma$, then the similarity degree of $\mathcal{A}$ is equal to $3$. In particular, the similarity degree of a $\mathcal{Z}$-stable, separable, non-nuclear, unital C${}^{\ast }$-algebra is equal to $3$.

arXiv commentarXiv admin note: text overlap with arXiv:1407.0664

References in corpus (1)

• Similarity problems and length