15 research outputs found
A Class of Distal Functions on Semitopological Semigroups
The norm closure of the algebra generated by the set and of
functions on 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 and (more generally) for the
discrete (additive) group of any countable ring. Finally, our results are
treated for a bicyclic semigroup.Comment: To appear in Methods Funct. Anal. Topolog