On the unitary group of the multiplier algebra\cr of the Razak algebra

Abstract

Let $\mathcal W $ be the Razak algebra, which is an example of a continuous scale ${\rm C}^*$-algebra with $K_*(\mathcal W ) = 0$ and unique trace. We show that the group $U(\mathcal M (\mathcal W ))$ is path connected in the norm topology.