Doubly stochastic operators with zero entropy

Bartosz Frej, Dawid Huczek

Published 2018-03-21Version 1

We study doubly stochastic operators with zero entropy. We generalize three famous theorems: the Rokhlin's theorem on genericity of zero entropy, the Kushnirenko's theorem on equivalence of discrete spectrum and nullity and the Halmos-von Neumann's theorem on representation of maps with discrete spectrum as group rotations.