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On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms

Author

Listed:
  • Liping Li

    (Fudan University
    Bielefeld University)

  • Hanlai Lin

    (Fudan University)

Abstract

This paper is devoted to characterizing so-called order isomorphisms intertwining the $$L^2$$ 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.

Suggested Citation

  • Liping Li & Hanlai Lin, 2023. "On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1304-1320, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01200-1
    DOI: 10.1007/s10959-022-01200-1
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    References listed on IDEAS

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    1. Kuwae, Kazuhiro, 2021. "Irreducible decomposition for Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 339-356.
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