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.
"Doubly stochastic operators with zero entropy." Ann. Funct. Anal. 10 (1) 144 - 156, February 2019. https://doi.org/10.1215/20088752-2018-0015