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arXiv · 2109.00615

Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms

Lorenzo Dello Schiavo·Melchior Wirth
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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.

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Lorenzo Dello Schiavo, Melchior Wirth. 2021-09-01. Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms. https://doi.org/10.1007/s00028-022-00859-7

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