A Class of Distal Functions on Semitopological Semigroups

Details A Class of Distal Functions on Semitopological Semigroups A Class of Distal Functions on Semitopological Semigroups

2009-02-13

arxiv.org/abs/0902.2358v1

Mathematics

Functional Analysis

To appear in Methods Funct. Anal. Topology

Scientific paper

The norm closure of the algebra generated by the set $\{n\mapsto {\lambda}^{n^k}:$ $\lambda\in{\mathbb {T}}$ and $k\in{\mathbb{N}}\}$ of functions on $({\mathbb {Z}}, +)$ was studied in \cite{S} (and was named as the Weyl algebra). In this paper, by a fruitful result of Namioka, this algebra is generalized for a general semitopological semigroup and, among other things, it is shown that the elements of the involved algebra are distal. In particular, we examine this algebra for $({\mathbb {Z}}, +)$ and (more generally) for the discrete (additive) group of any countable ring. Finally, our results are treated for a bicyclic semigroup.

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