A universal hypercyclic representation

Some new examples of universal hypercyclic operators in the sense of Glasner and Weiss

A bounded operator on a real or complex separable infinite-dimensional Banach space $Z$ is universal in the sense of Glasner and Weiss if for every invertible ergodic measure-preserving transformation $T$ of a standard Lebesgue probability space $(X,\mathcal {B},μ)$, there exists an $A$-invariant probability measure $ν$ on $H$ with full support such that the two dynamical systems $(X,\mathcal {B},μ;T)$ and $(H,\mathcal {B}_{H},ν;A)$ are isomorphic. We present a general and simple criterion for an operator to be universal, which allows us to characterize universal operators among unilateral or …