Complex Dirichlet Forms: Non symmetric Diffusion Processes and Schoedinger Operators

The concept of complex Dirichlet forms epsilon_c resp.operators L_c in complex weighted L^2-spaces is introduced. Perturbations of classical Dirichlet forms by forms associated with complex first-order differential operators provide examples of complex Dirichlet forms. Complex Dirichlet operators L_c are unitarily equivalent with (a family of) Schroedinger operators with electromagnetic potentials. To epsilon_c there is associated a pair of real-valued non symmetric Dirichlet forms on the corresponding real weighted L^2-spaces, which in turn are associated with (non-symmetric) diffusion processes. Results by Stannat on non symmetric Dirichlet forms and their perturbations can be used for discussing the essential self-adjointness of L_c. New closability criteria for (perturbation of) non symmetric Dirichlet forms are obtained.