A Modified Similarity Degree for C*-algebras

We define variants of Pisier's similarity degree for unital C*-algebras and use direct integral theory to obtain new results. We prove that if every II$_{1}$ factor representation of a separable C*-algebra $\mathcal{A}$ has property $Γ$, then the similarity degree of $\mathcal{A}$ is at most 11.

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