Hi,

Given a $\sigma$-unital $C^*$-algebra $A$ and a full Hilbert $A$-module $E$, is it possible to find an approximate unit $ \{\epsilon_i\}, i\in I$ in $A$ such that each $\epsilon_i$ is of the form $< e_i,e_i>_A$, where $e_i \in E, \forall i\in I$? If not, what are the conditions on $E$ and $A$ for which this might be possible?

Thanks in advance.