Let $H$ be a complex, separable Hilbert space and $\mathcal{B}(H)$ denote the algebra of bounded linear operators on $H$. Let $A \subset \mathcal{B}(H)$ by a subalgebra. I'm looking for some conditions for $A$ to be weakly (operator) dense in $\mathcal{B}(H)$. I've been looking in books like Arveson, Murphy and Conway and I can't find anything.
Anyone can help me?