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On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms

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Abstract

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.

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Acknowledgements

The authors would like to thank the anonymous referees for many helpful suggestions which greatly improved this article. The first named author is partially supported by NSFC (No. 11931004) and the Alexander von Humboldt Foundation in Germany.

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The first named author is partially supported by NSFC (No. 11931004) and the Alexander von Humboldt Foundation in Germany.

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  1. School of Mathematical Sciences, Fudan University, Shanghai, China

    Liping Li & Hanlai Lin

  2. Department of Mathematics, Bielefeld University, Bielefeld, Germany

    Liping Li

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  1. Liping Li
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  2. Hanlai Lin
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Hanlai Lin wrote the main manuscript text and Liping Li modified the text.

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Correspondence to Hanlai Lin.

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Li, L., Lin, H. On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms. J Theor Probab 36, 1304–1320 (2023). https://doi.org/10.1007/s10959-022-01200-1

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