  Let $\Omega \subset {\bf R}^d$ be a bounded open set with Lipschitz boundary
$\Gamma$. It will be shown that the Jordan chains of m-sectorial second-order
elliptic partial differential operators with measurable coefficients and (local
or non-local) Robin boundary conditions in $L_2(\Omega)$ can be characterized
with the help of Jordan chains of the Dirichlet-to-Neumann map and the boundary
operator from $H^{1/2}(\Gamma)$ into $H^{-1/2}(\Gamma)$. This result extends
the Birman--Schwinger principle in the framework of elliptic operators for the
characterization of eigenvalues, eigenfunctions and geometric eigenspaces to
the complete set of all generalized eigenfunctions and algebraic eigenspaces.
