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.
Cite
@article{arxiv.1005.0230,
title = {On Hilbert dynamical systems},
author = {Eli Glasner and Benjamin Weiss},
journal= {arXiv preprint arXiv:1005.0230},
year = {2014}
}