| Résume | 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 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. |
