West semigroups as compactifications of locally compact abelian groups

Elgun E. E.

SEMIGROUP FORUM, vol.93, no.1, pp.71-85, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 93 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1007/s00233-015-9747-8
  • Journal Name: SEMIGROUP FORUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.71-85
  • Acibadem Mehmet Ali Aydinlar University Affiliated: No

Abstract

In this paper, we will identify certain subsemigroups of the unit ball of as semitopological compactifications of locally compact abelian groups, using an idea of West (Proc R Ir Acad Sect A 67:27-37, 1968). Our result has been known for the additive group of integers since Bouziad et al. (Semigr Forum 62(1):98-102, 2001). We will construct a semitopological semigroup compactification for each locally compact abelian group G, depending on the algebraic properties of G. These compact semigroups can be realized as quotients of both the Eberlein compactification , and the weakly almost periodic compactification, , of G. The concrete structure of these compact quotients allows us to gain insight into known results by Brown (Bull Lond Math Soc 4:43-46, 1972) and Brown and Moran (Proc Lond Math Soc 22(3):203-216, 1971) and by Bordbar and Pym (Math Proc Camb Philos Soc 124(3):421-449, 1998), where for the groups and , it is proved that and contain uncountably many idempotents and the set of idempotents is not closed.