H. R. Vishki

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Articles: 1

A class of distal functions on semitopological semigroups

A. Jabbari, H. R. E. Vishki

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 15 (2009), no. 2, 188-194

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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