Are all hyperlinear traces MF?

Determine whether, for every C*-algebra A, every hyperlinear trace on A is an MF trace.

Background

The paper identifies the status of hyperlinear traces (those factoring through ultraproducts such as R^ω or ∏M_n/⊕_2 M_n) as largely unresolved with respect to being MF traces (admitting uniform norm-multiplicative finite-dimensional approximations).

Recent progress includes that hyperlinear traces on cone C*-algebras are MF, and this work extends such results via homotopy methods: if A is homotopy dominated by a nuclear C*-algebra B and all (hyperlinear) traces on B are MF, then all hyperlinear traces on A are MF (Corollary 4.16). The general problem, however, remains open.