Séminaires : Séminaire Général de Logique

Equipe(s) : lm,
Responsables :S. Anscombe, A. Khélif, A. Vignati
Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr
Salle : 1013
Adresse :Sophie Germain

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Abonnement à la liste de diffusion

Orateur(s) Slawomir Solecki - Cornell,
Titre Closed subgroups generated by generic measure preserving transformations
Horaire16:00 à 17:15
Diffusion https://u-paris.zoom.us/rec/share/OyCgdp5b1f_-pDPiNXjXyZ_x4enPhPIxfeFLvo0DDVID1sJY7Wq27oLew0TAJHc.-jCtsYcv5WSBxs1P?startTime=1620223331000
RésumeWe describe the background and outline a proof of the following theorem: 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 $\mathbb T$. 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, an important role is played by a new mean ergodic theorem for ergodic boolean actions of $L^0(\lambda, {\mathbb T})$.
AdresseSophie Germain