Published online by Cambridge University Press: 07 January 2019
We give two characterisations of tracially nuclear C*-algebras. The first is that the finite summand of the second dual is hyperfinite. The second is in terms of a variant of the weak* uniqueness property. The necessary condition holds for all tracially nuclear C*-algebras. When the algebra is separable, we prove the sufficiency.
The first three authors are, respectively, supported by a Collaboration Grant from the Simons Foundation, a Faculty Development Grant from Columbia College Chicago and a Dissertation Year Fellowship from the University of New Hampshire.