Ergodic decompositions of Dirichlet forms under order isomorphisms

We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two q...

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Detalles Bibliográficos
Autores principales: Dello Schiavo, Lorenzo, Wirth, Melchior
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9803614/
https://www.ncbi.nlm.nih.gov/pubmed/36597554
http://dx.doi.org/10.1007/s00028-022-00859-7
Descripción
Sumario:We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.

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