A Class of Distal Functions on Semitopological Semigroups

The norm closure of the algebra generated by the set n � � n k : � ∈ and k ∈ of functions on ( ,+) was studied in (11) (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 ( ,+) and (more generally) for the discrete (additive) group of any countable ring. Finally, our results are treated for a bicyclic semigroup.