On order isomorphisms intertwining semigroups for Dirichlet forms
Functional Analysis
2022-04-08 v1 Probability
Abstract
This paper is devoted to characterizing the so-called order isomorphisms intertwining the -semigroups of two Dirichlet forms. We first show that every unitary order isomorphism intertwining semigroups is the composition of -transformation and quasi-homeomorphism. In addition, under the absolute continuity condition on Dirichlet forms, every (not necessarily unitary) order isomorphism intertwining semigroups is the composition of -transformation, quasi-homeomorphism, and multiplication by a certain step function.
Cite
@article{arxiv.2204.02975,
title = {On order isomorphisms intertwining semigroups for Dirichlet forms},
author = {Liping Li and Hanlai Lin},
journal= {arXiv preprint arXiv:2204.02975},
year = {2022}
}