Suppose $A$ is a $C^*$-algebra, $A^\prime$ is a non-degenerate $C^*$-subalgebra of $A$. What is the definition of non-degenerate $C^*$-subalgebra? Is it defined as following :
There exists an inclusion $l:A^\prime \to M(A)$ such that $l(A^\prime)(A)$ is dense in $A$?