Left quotients of a C*-algebra, III: Operators on left quotients

Abstract

Let $L$ be a norm closed left ideal of a $C^*$-algebra $A$. Then the left quotient $A/L$ is a left $A$-module. In this paper, we shall implement Tomita's idea about representing elements of $A$ as left multiplications: $\pi _p(a)(b+L)=ab+L$. A complete ch