Entropy of subshifts and the Macaev norm

Abstract

We obtain the exact value of Voiculescu's invariant $k_{\infty }^{-}\left(\tau \right)$, which is an obstruction of the existence of quasicentral approximate units relative to the Macaev ideal in perturbation theory, for a tuple $\tau$ 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.