Bartosz Frej, Dawid Huczek. Source: Annals of Functional Analysis, Volume 10, Number 1, 144--156.Abstract:
We study doubly stochastic operators with zero entropy. We generalize three famous theorems: Rokhlin’s theorem on genericity of zero entropy, Kushnirenko’s theorem on equivalence of discrete spectrum and nullity, and Halmos–von Neumann’s theorem on representation of maps with discrete spectrum as group rotations.