Let $E$ be a Hilbert $A$-module. Then, $E\langle E,E\rangle$ is norm dense in $E$.
I am having trouble proving this. I believe $\langle E,E\rangle $ is a $C^*$-algebra. If I can show this, then the proof is easy since all $C^*$-algebras have an approximate identity.
It seems like it shouldn't be too hard, but I am having trouble showing it.