On Hilbert dynamical systems

Abstract

Returning to a classical question in Harmonic Analysis we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers Z which is not in the norm-closure of the algebra B(Z) of Fourier-Stieltjes transforms of measures on the circle, the dual group of Z, and which is recurrent. We also show that there is a Polish monothetic group which is reflexively but not Hilbert representable.