Similarity Degree of a Class of C-Algebras

Academic Article


  • Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-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$^*$-$\Gamma$, 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$^*$-algebra is equal to $3$.
  • Authors

  • Qian, Wenhua
  • Shen, Junhao
  • Status

    Publication Date

  • January 2016
  • Has Subject Area


  • Property Gamma
  • Similarity degree
  • Similarity problem
  • Digital Object Identifier (doi)

    Start Page

  • 121
  • End Page

  • 149
  • Volume

  • 84
  • Issue

  • 1