Prof. Stefaan Vaes | Ergodic states on type III_1 factors and ergodic actions скачать в хорошем качестве

Prof. Stefaan Vaes | Ergodic states on type III_1 factors and ergodic actions

Speaker(s): Professor Stefaan Vaes (KU Leuven) Date: 26 June 2023 - 10:00 to 11:00 Venue: INI Seminar Room 1 Session Title: Ergodic states on type III_1 factors and ergodic actions Event: [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.