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A class of distal functions on semitopological semigroups

Abstract

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.

Article Information

 Title A class of distal functions on semitopological semigroups Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 2, 188-194 MathSciNet MR2553534 Copyright The Author(s) 2009 (CC BY-SA)

Authors Information

A. Jabbari
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran

H. R. E. Vishki
Department of Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran; Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, Iran

Citation Example

A. Jabbari and H. R. E. Vishki, A class of distal functions on semitopological semigroups, Methods Funct. Anal. Topology 15 (2009), no. 2, 188-194.

BibTex

@article {MFAT464,
AUTHOR = {Jabbari, A. and Vishki, H. R. E.},
TITLE = {A class of distal functions on semitopological semigroups},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {2},
PAGES = {188-194},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=464},
}