English

On Hilbert dynamical systems

Dynamical Systems 2014-02-25 v1 Functional Analysis Group Theory

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.

Keywords

Cite

@article{arxiv.1005.0230,
  title  = {On Hilbert dynamical systems},
  author = {Eli Glasner and Benjamin Weiss},
  journal= {arXiv preprint arXiv:1005.0230},
  year   = {2014}
}
R2 v1 2026-06-21T15:17:43.354Z