A geometrical approach to the Gorini-Kossakowski-Sudarshan-Lindblad generation theorem

I develop a rigorous "geometrical" approach to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generation theorem, which is the answer to the question: which superoperators generate completely positive (CP) evolutions? The fundamental tool in the present approach is a basis-free relative of the Choi-Jamiolkowski isomorphism which, for the finite-dimensional case, allows access to geometrical properties of the set of CP superoperators through corresponding properties of the proper cone of positive operators in a real Hilbert space of hermitian operators. Such properties include extremal decomposition (Kraus form) and characterization of "tangent" vectors. The latter smoothly yields a version of the GKSL theorem, even for time-inhomogeneous evolution. The infinite-dimensional case is handled via a sequence of finite-dimensional approximations. This approach allows a self-contained proof requiring only basic tools of functional analysis.