Inner quasidiagonality and strong NF algebras

Bruce Blackadar and Eberhard Kirchberg

Vol. 198 (2001), No. 2, 307–329

DOI: 10.2140/pjm.2001.198.307

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.

Milestones

Received: 5 January 1996

Revised: 20 December 1998

Published: 1 April 2001