Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

The uniform compactification of a locally compact abelian group

M. Filalia1*

a1 Department of Mathematics, University of Sheffield

In recent years, the Stone-Čech compactification of certain semigroups (e.g. discrete semigroups) has been an interesting semigroup compactification (i.e. a compact right semitopological semigroup which contains a dense continuous homomorphic image of the given semigroup) to study, because an Arens-type product can be introduced. If G is a non-compact and non-discrete locally compact abelian group, then it is not possible to introduce such a product into the Stone-Čech compactification βG of G (see [1]). However, let UC(G) be the Banach algebra of bounded uniformly continuous complex functions on G, and let UG be the spectrum of UC(G) with the Gelfand topology. If fxs2208 UC(G), then the functions f and fy defined on G by

S0305004100069413_eqnU1

are also in UC(G).

(Received January 23 1990)

Footnotes

* Current address: Department of Mathematics, University of Oulu, 90570, Finland.