AN ALGEBRA WHOSE SUBALGEBRAS ARE CHARACTERIZED BY DENSITY
Résumé
Abstract We refine a construction of Choi, Farah, and Ozawa to build a nonseparable amenable operator algebra ${\rm {\cal A}}$ ⊆ ℓ ∞ ( M 2 ) 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.