Inner quasidiagonality and strong NF algebras

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.