It is well known that in every von Neumann algebra $\mathcal{M}$, the left annihilator of a given subset $S\subseteq \mathcal{M}$ is in the form $\mathcal{M}p$ for some projection $p$ in $\mathcal{M}$.
By a dual operator algebra $\mathcal{A}$, we mean a WOT-closed subalgebra of operators on some Hilbert space $H$.
Q. Does there exist any similar characterization of the left annihilators in dual operator algebras?
Contained an answer with a mistake, but I can't delete because the OP does not unaccept the question.