On order isomorphisms intertwining semigroups for Dirichlet forms
Liping Li, Hanlai Lin

TL;DR
This paper characterizes order isomorphisms that intertwine semigroups of Dirichlet forms, revealing their structure as compositions of transformations, quasi-homeomorphisms, and step functions under certain conditions.
Contribution
It provides a detailed description of the structure of order isomorphisms intertwining Dirichlet form semigroups, including the effects of absolute continuity conditions.
Findings
Unitary order isomorphisms are compositions of $h$-transformation and quasi-homeomorphism.
General order isomorphisms are compositions of $h$-transformation, quasi-homeomorphism, and step functions.
The characterization applies under specific conditions like absolute continuity.
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.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals
