The quasitrace conjecture for arbitrary C*-algebras

A quasitrace on a C*-algebra is a map satisfying the usual positivity, partial additivity, and matrix-extension properties of a quasitrace; a trace is a linear quasitrace. In particular, quasitraces extend traces on abelian C*-subalgebras and satisfy $q(AA^*)=q(A^*A)$.

Quasitrace conjecture. Quasitraces on arbitrary C*-algebras are traces.

The paper states this as a consequence of Kaplansky's conjecture and attributes the implication to Haagerup. It is therefore a related conjectural claim, but the supplied text does not state whether it has been resolved.