We obtain the exact value of Voiculescu's invariant , which is an obstruction of the existence of quasicentral approximate units relative to the Macaev ideal in perturbation theory, for a tuple of operators in the following two classes: (1) creation operators associated with a subshift, which are used to define Matsumoto algebras, (2) unitaries in the left regular representation of a finitely generated group.
Rui OKAYASU. "Entropy of subshifts and the Macaev norm." J. Math. Soc. Japan 56 (1) 177 - 191, January, 2004. https://doi.org/10.2969/jmsj/1191418701