Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms
arXiv:2109.00615 · doi:10.1007/s00028-022-00859-7
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.
16 pages. To appear in J. Evol. Equ. arXiv admin note: text overlap with arXiv:2003.01366