  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 $(X,\mathcal {B},\mu )$, there exists an $A$-invariant
probability measure $\nu $ on $H$ with full support such that the two dynamical
systems $(X,\mathcal {B},\mu ;T)$ and $(H,\mathcal {B}_{H},\nu ;A)$ 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 bilateral weighted shifts on $\ell_{p}$ or $c_{0}$, show the existence of
universal operators on a large class of Banach spaces, and give a criterion for
universality in terms of unimodular eigenvectors. We also obtain similar
results for operators which are universal for all ergodic systems (not only for
invertible ones), and study necessary conditions for an operator on a Hilbert
space to be universal.

Dynamical Systems;Functional Analysis