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arXiv · 0902.2358

A Class of Distal Functions on Semitopological Semigroups

A. Jabbari·H. R. E. Vishki
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Abstract

The norm closure of the algebra generated by the set $\{n\mapsto λ^{n^k}:$ $λ\in{\mathbb {T}}$ 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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BibTeXRIS

A. Jabbari, H. R. E. Vishki. 2009-02-13. A Class of Distal Functions on Semitopological Semigroups. https://arxiv.org/abs/0902.2358

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