Complex dirichlet forms: Non symmetric diffusion processes and Schrodingeroperators

The concept of complex Dirichlet forms epsilon(c) resp. operators L-c in co mplex weighted L-2-spaces is introduced. Perturbations of classical Dirichl et forms by forms associated with complex first-order differential operator s provide examples of complex Dirichlet forms. Complex Dirichlet operators L-c are unitarily equivalent with (a family of) Schrodinger operators with electromagnetic potentials. To epsilon(c) there is associated a pair of real-valued non symmetric Diric hlet 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 form s are obtained.