Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms
Functional Analysis
2023-01-10 v2 Probability
Abstract
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.
Cite
@article{arxiv.2109.00615,
title = {Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms},
author = {Lorenzo Dello Schiavo and Melchior Wirth},
journal= {arXiv preprint arXiv:2109.00615},
year = {2023}
}
Comments
16 pages. To appear in J. Evol. Equ. arXiv admin note: text overlap with arXiv:2003.01366