  Given a pair of self-adjoint-preserving completely bounded maps on the same
$C^*$-algebra, say that $\varphi \leq \psi$ if the kernel of $\varphi$ is a
subset of the kernel of $\psi$ and $\psi \circ \varphi^{-1}$ is completely
positive. The \emph{Agler class} of a map $\varphi$ is the class of $\psi \geq
\varphi.$ Such maps admit colligation formulae, and, in Lyapunov type
situations, transfer function type realizations on the Stinespring coefficients
of their Wittstock decompositions. As an application, we prove that the support
of an extremal Wittstock decomposition is unique.
