In this note we show that a separable C*-algebra is nuclear and has a quasidiagonal extension by K: (the ideal of compact operators on an infinite-dimensional separable Hilbert space) if and only if it is a nuclear finite algebra (NF-algebra) in the sense of Blackadar and Kirchberg, and deduce that every nuclear C*-subalgebra of a NF-algebra is NF. We show that strong NF-algebras satisfy a Fr type condition.
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