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Ergodic states on type III_1 factors and ergodic actions

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OASW05 - OAS Follow on: Operator Algebras: Subfactors and Applications

I will report on a joint work with Amine Marrakchi. Since the early days of Tomita-Takesaki theory, it is known that a von Neumann algebra that admits a state with trivial centralizer must be a type III 1 factor, but the converse remained open. I will present a solution of this problem, proving that such ergodic states form a dense G\delta set among all faithful normal states on any III _1 factor with separable predual. Through Connes’ Radon-Nikodym cocycle theorem, this problem is related to the existence of ergodic cocycle perturbations for outer group actions, which I will discuss in the second half of the talk.

This talk is part of the Isaac Newton Institute Seminar Series series.

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