A note on quasi-similarity of Koopman operators
arXiv:0903.3109 · doi:10.1112/jlms/jdq029
Abstract
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.
15 pages