Let $A$ be a C*-algebra. According to operator algebraists, it is well known that $A$ embeds into the atomic part of its double dual in the following sense: if $z$ is the central projection in $A^{**}$ onto its atomic part, then the composition of the embedding $A \hookrightarrow A^{**}$ with multiplication by $z$ yields an embedding $A \hookrightarrow zA^{**}$.

I see how one can prove this, but I need this result in my paper which is not aimed at operator algebraists, so I would like to give a reference. However, I cannot find this in the literature. I looked at Takesaki, Blackadar, Dixmier, Sakai, Kadison-Ringrose, and the closest I got was Definition III.6.35 in Takesaki where he defines the universal atomic representation, but I don't see how the above result immediately follows from this definition or its subsequent results.

Does anyone have a reference for this?