1.
J Evol Equ
; 23(1): 9, 2023.
Article
in English
| MEDLINE
| ID: mdl-36597554
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.