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• W3137600114 abstract "We show that, for a generic measure preserving transformation $T$, the closed group generated by $T$ is not isomorphic to the topological group $L^0(lambda, {mathbb T})$ of all Lebesgue measurable functions from $[0,1]$ to $mathbb T$ (taken with pointwise multiplication and the topology of convergence in measure). This result answers a question of Glasner and Weiss. The main step in the proof consists of showing that Koopman representations of ergodic boolean actions of $L^0(lambda, {mathbb T})$ possess a non-trivial property not shared by all unitary representations of $L^0(lambda, {mathbb T})$. In proving that theorem, we use an ergodic theorem for ergodic boolean actions of $L^0(lambda, {mathbb T})$ also established in the present paper. The main tool underlying our arguments is a theorem on the form of unitary representations of $L^0(lambda, {mathbb T})$ from our earlier work." @default.
• W3137600114 created "2021-03-29" @default.
• W3137600114 creator A5012953076 @default.
• W3137600114 date "2021-03-17" @default.
• W3137600114 modified "2023-09-27" @default.
• W3137600114 title "Closed subgroups generated by generic measure preserving transformations" @default.
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• W3137600114 hasPublicationYear "2021" @default.
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