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On Hilbert dynamical systems

Published online by Cambridge University Press:  13 June 2011

ELI GLASNER  and
BENJAMIN WEISS
ELI GLASNER
Affiliation:
Department of Mathematics, Tel Aviv University, Tel Aviv, Israel (email: glasner@math.tau.ac.il)
BENJAMIN WEISS
Affiliation:
Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, Israel (email: weiss@math.huji.ac.il)
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Abstract

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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 dual group $\hat {\mathbb {Z}}=\mathbb {T}$, and which is recurrent. We also show that there is a Polish monothetic group which is reflexively but not Hilbert representable.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 629 - 642
Copyright
Copyright © Cambridge University Press 2011

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