As in Blackadar's "Operator Algebras" Definition II.4.1.1., call an approximate unit $(a_\lambda)$ in the positive unit ball of a C*-algebra _almost idempotent_ if $a_\lambda a_\gamma=a_\lambda$ whenever $\lambda<\gamma$.

$$\text{Does every C*-algebra have an almost idempotent approximate unit?}$$