On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms.

This paper is devoted to characterizing so-called order isomorphisms intertwining the L 2 -semigroups of two quasi-regular Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of h-transformation and quasi-homeomorphism. In addition, under the assumption that the underlying spaces admit so-called irreducible decompositions for Dirichlet forms, every (not necessarily unitary) order isomorphism intertwining semigroups can be expressed as the composition of h-transformation, quasi-homeomorphism and multiplication by a certain step function. [ABSTRACT FROM AUTHOR]