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 -theory sufficient condition for generalized quasidiagonality of certain extensions of simple continuous-scale -algebras, including certain continuous-scale hereditary -subalgebras of the stabilized Jiang–Su algebra.
"Generalized quasidiagonality for extensions." Banach J. Math. Anal. 13 (3) 582 - 598, July 2019. https://doi.org/10.1215/17358787-2019-0005