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\({^*}\)-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.
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The first author was supported by Research Center for Operator Algebras of East China Normal University.
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Qian, W., Shen, J. Similarity Degree of a Class of C\({^*}\)-Algebras. Integr. Equ. Oper. Theory 84, 121–149 (2016). https://doi.org/10.1007/s00020-015-2266-x
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DOI: https://doi.org/10.1007/s00020-015-2266-x