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AN ALGEBRA WHOSE SUBALGEBRAS ARE CHARACTERIZED BY DENSITY
ALESSANDRO VIGNATI
Journal:

The Journal of Symbolic Logic / Volume 80 / Issue 3 / September 2015

Published online by Cambridge University Press:

22 July 2015, pp. 1066-1074

Print publication:

September 2015
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We refine a construction of Choi, Farah, and Ozawa to build a nonseparable amenable operator algebra ${\rm {\cal A}}$ ⊆ ℓ∞ (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.