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
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author Dello Schiavo, Lorenzo
Wirth, Melchior
author_facet Dello Schiavo, Lorenzo
Wirth, Melchior
author_sort Dello Schiavo, Lorenzo
collection PubMed
description 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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spelling pubmed-98036142023-01-01 Ergodic decompositions of Dirichlet forms under order isomorphisms Dello Schiavo, Lorenzo Wirth, Melchior J Evol Equ Article 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. Springer International Publishing 2022-12-30 2023 /pmc/articles/PMC9803614/ /pubmed/36597554 http://dx.doi.org/10.1007/s00028-022-00859-7 Text en © The Author(s) 2022, corrected publication 2023corrected publication 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Dello Schiavo, Lorenzo
Wirth, Melchior
Ergodic decompositions of Dirichlet forms under order isomorphisms
title Ergodic decompositions of Dirichlet forms under order isomorphisms
title_full Ergodic decompositions of Dirichlet forms under order isomorphisms
title_fullStr Ergodic decompositions of Dirichlet forms under order isomorphisms
title_full_unstemmed Ergodic decompositions of Dirichlet forms under order isomorphisms
title_short Ergodic decompositions of Dirichlet forms under order isomorphisms
title_sort ergodic decompositions of dirichlet forms under order isomorphisms
topic Article
url 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
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