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.