About completeness of $pH+qH$.

Question

I readied a notes of Functional Analysis and I see the follow definition: $$ p\vee q=\overline{pH+qH} $$ where $H$ is a Hilbert space, $p,q\in B(H)$ are projections ($p=p^2=p^*$), more precisely, $pH$ and $qH$ are the image of $p$ and $q$ (resp.). The doubt is: why is necessary input the closure? $pH$ and $qH$ is clearly closed, since are image of projections, but there is a example of $pH+qH$ that is not closed? I didn't found other mentions about it (like questions or the like)