The Hilbert-space conjecture for irreducible energy forms

Let $E$ be an irreducible energy form with domain $D(E)$ and kernel $\ker E$. Hilbert-space conjecture. The quotient $(D(E)/\ker E,E)$ is a Hilbert space. This conjecture concerns when the quotient induced by an irreducible energy form is complete; the supplied source does not state whether it has been resolved.