2009/02/13 by Jabbari, A., Vishki, H. R. E.
#43A60 #54C35 #54H20 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.0902.2358
The norm closure of the algebra generated by the set \n↦ λnk: λ∈\mathbb T and k∈ℕ\ of functions on (\mathbb Z, +) was studied in \citeS (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.