{"scopus_import":"1","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-01-08T23:00:53Z","oa_version":"Published Version","oa":1,"status":"public","quality_controlled":"1","title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","date_updated":"2023-06-28T11:54:35Z","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"01","article_processing_charge":"Yes (via OA deal)","day":"01","license":"https://creativecommons.org/licenses/by/4.0/","type":"journal_article","file":[{"date_updated":"2023-01-20T10:45:06Z","date_created":"2023-01-20T10:45:06Z","file_size":422612,"file_id":"12325","success":1,"relation":"main_file","checksum":"1f34f3e2cb521033de6154f274ea3a4e","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","creator":"dernst","access_level":"open_access","content_type":"application/pdf"}],"abstract":[{"text":"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.","lang":"eng"}],"department":[{"_id":"JaMa"}],"issue":"1","date_published":"2023-01-01T00:00:00Z","publication_status":"published","year":"2023","volume":23,"intvolume":"        23","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208"},{"grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups"}],"ddc":["510"],"acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","isi":1,"file_date_updated":"2023-01-20T10:45:06Z","publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"external_id":{"isi":["000906214600004"]},"publication":"Journal of Evolution Equations","author":[{"orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","first_name":"Melchior"}],"has_accepted_license":"1","doi":"10.1007/s00028-022-00859-7","_id":"12104","article_number":"9","language":[{"iso":"eng"}],"citation":{"ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>"},"article_type":"original","ec_funded":1}