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A bounded operator on a real or complex separable infinite-dimensional Banachspace $Z$ is universal in the sense of Glasner and Weiss if for everyinvertible ergodic measure-preserving transformation $T$ of a standard Lebesgueprobability space $(X,\mathcal {B},\mu )$, there exists an $A$-invariantprobability measure $\nu $ on $H$ with full support such that the two dynamicalsystems $(X,\mathcal {B},\mu ;T)$ and $(H,\mathcal {B}_{H},\nu ;A)$ areisomorphic. We present a general and simple criterion for an operator to beuniversal, which allows us to characterize universal operators among unilateralor bilateral weighted shifts on $\ell_{p}$ or $c_{0}$, show the existence ofuniversal operators on a large class of Banach spaces, and give a criterion foruniversality in terms of unimodular eigenvectors. We also obtain similarresults for operators which are universal for all ergodic systems (not only forinvertible ones), and study necessary conditions for an operator on a Hilbertspace to be universal.

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