Let $M$ be a W\*-algebra. I am looking for the proof of the following fact:


Let $z$ be the supremum of minimal projections in $M$. Then $z$ is central. 



Minimal central projection in W*-algebras
It is enough to show that $z$ commutes to all unitaries. But if $p$ is a minimal projection then $upu^{-1}$ is again a minimal projection.


