Quasi-regular Dirichlet Forms and Markov Processes

We identify an analytic property of a (non-symmetric) Dirichlet form on a general (topological state space called "quasi-regularity" which we prove to be equivalent with the existence of an associated standard Markov process, respectively the existence of an associated pair of right processes. In addition, we prove a one to one correspondence between all quasi-regular Dirichlet forms and all (equivalence classes of) pairs of "m-sectorial" right processes.