I am reading a book about C*-algebra. I encounter a theorem without proof. Could someone help me to complete its proof or give me some hints.
Theorem 2.1. Let $I$ be an ideal of C*-algebra $A$. Then $I$ has an approximate unit $\{e_{i}\}\subset I$ such that $||e_{i}a-ae_{i}|| \rightarrow 0$, as $i\rightarrow \infty$, for all $a\in A$. In fact, if $\{f_{k}\}\subset I$ is any approximate unit for $I$ then a quasicentral approximate unit can always be extracted fromm its convex hull.
Here, quasicentral approximate units: An approximate unit $\{e_{i}\}$ for $I$ which asymptotically commutes with all elements of $A$, i.e. $||xe_{i}-e_{i}x||\rightarrow 0$, for all $x\in A$.
If you have access to Davidson's "C$^*$-Algebras by Example", it is Theorem I.9.16 there. If you don't, I'll try to post the proof later, but it is a one-page+ affair.