On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms

Liping Li () and Hanlai Lin ()
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Liping Li: Fudan University
Hanlai Lin: Fudan University

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 1304-1320

Abstract: 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.

Keywords: Dirichlet forms; Order isomorphisms intertwining semigroups; h-transformations; Quasi-homeomorphisms; Irreducible decomposition; 60J46; 60J35; 31C25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01200-1

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