A note on quasi-similarity of Koopman operators
classification
🧮 math.DS
math.FA
keywords
automorphismsergodickoopmanmarkovquasi-similarityansweringassociatedclass
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Answering a question of A. Vershik we construct two non-weakly isomorphic ergodic automorphisms for which the associated unitary (Koopman) representations are Markov quasi-similar. We also discuss metric invariants of Markov quasi-similarity in the class of ergodic automorphisms.
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