Abstract

Continuing the study of generalized inductive limits of finite-dimensional C^*-algebras, we define a refined notion of quasidiagonality for C^*-algebras, called inner quasidiagonality, and show that a separable C^*-algebra is a strong NF algebra if and only if it is nuclear and inner quasidiagonal. Many natural classes of NF algebras are strong NF, including all simple NF algebras, all residually finite-dimensional nuclear C^*-algebras, and all approximately subhomogeneous C^*-algebras. Examples are given of NF algebras which are not strong NF.

Authors