Abstract
While the Koopman representation can be used to distinguish many types of p.m.p. actions, it cannot distinguish nontrivial Bernoulli actions over an infinite group, as one always gets infinitely many copies of the left regular representation, along with a copy of the trivial representation (see Section 1.3).
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Kerr, D., Li, H. (2016). Entropy for Actions of Amenable Groups. In: Ergodic Theory. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-49847-8_9
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DOI: https://doi.org/10.1007/978-3-319-49847-8_9
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