Extensions of dissipative operators with closable imaginary part

Given a dissipative operator $A$ on a complex Hilbert space $mathcal{H}$ such that the quadratic form $fmapsto mbox{Im}langle f,Afrangle$ is closable, we give a necessary and sufficient condition for an extension of $A$ to still be dissipative. As applications, we describe all maximally accretive extensions of strictly positive symmetric operators and all maximally dissipative extensions of a highly singular first-order operator on the interval.