Suppose that $H_1$ and $H_2$ are Hilbert spaces and $T: H_1 \to H_2$ is a densely defined linear map with closed graph. Show that $T = T^{**}$.
(I have shown that such a $T$ has a densely defined adjoint $T^*$. And as such, $T^{**}$ makes sense since $T^*$ has closed graph.)