Mixing operators with prescribed unimodular eigenvectors

Ergodic Theory and Dynamical Systems, 42 (2022), 1-8 For arbitrary closed countable subsets $Z$ of the unit circle examples of topologically mixing operators on Hilbert spaces are given which have a densely spanning set of unimodular eigenvectors with eigenvalues restricted to $Z$. In particular, these operators cannot be ergodic in the Gaussian sense.