A multiplicative ergodic theorem for von Neumann algebra valued cocycles

Ben Hayes
University of Virginia
Mathematics

I will discuss joint work with Lewis Bowen and Frank Lin. In it, we prove a generalization of the classical multiplicative ergodic theorem due to Osoledets. Our multiplicative ergodic theorem works for cocycles valued in the group of invertible elements of a finite von Neumann algebra, and crucially uses a CAT(0) space associated to a tracial von Neumann algebra. Our work appears to be the first case where one can prove a multiplicative ergodic theorem in the setting that the limiting operator can have continuous spectrum.