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We refine a construction of Choi, Farah, and Ozawa to build a nonseparable amenable operator algebra ${\rm {\cal A}}$ (M2) whose nonseparable subalgebras, including ${\rm {\cal A}}$ , are not isomorphic to a C*-algebra. This is done using a Luzin gap and a uniformly bounded group representation.

Next, we study additional properties of ${\rm {\cal A}}$ and of its separable subalgebras, related to the Kadison Kastler metric.



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