The corona theorem and Bass stable rank for $M(D(\sum_{i=1}^k a_i \delta_{\zeta_i}))$

Abstract

In this paper, we prove the corona theorem for $M(D(\mu_k))$ in two different ways, where $\mu_k = \sum_{i=1}^k a_i \delta_{\zeta_i}$. Then we prove that the Bass stable rank of $M(D(\mu_k))$ is one.