Abstract

We generalize the notion of quasidiagonality, for extensions, allowing for the case where the canonical ideal has few projections. We prove that the pointwise-norm limit of generalized quasidiagonal extensions is generalized quasidiagonal. We also provide a K-theory sufficient condition for generalized quasidiagonality of certain extensions of simple continuous-scale C∗-algebras, including certain continuous-scale hereditary C∗-subalgebras of the stabilized Jiang–Su algebra.

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