  Let $A$ and $(-\widetilde{A})$ be dissipative operators on a Hilbert space
$\mathcal{H}$ and let $(A,\widetilde{A})$ form a dual pair, i.e.
$A\subset\widetilde{A}^*$, resp.\ $\widetilde{A}\subset A^*$. We present a
method of determining the proper dissipative extensions $\widehat{A}$ of this
dual pair, i.e. $A\subset \widehat{A}\subset\widetilde{A}^*$ provided that
$\mathcal{D}(A)\cap\mathcal{D}(\widetilde{A})$ is dense in $\mathcal{H}$.
  Applications to symmetric operators, symmetric operators perturbed by a
relatively bounded dissipative operator and more singular differential
operators are discussed.
  Finally, we investigate the stability of the numerical range of the different
dissipative extensions.
