Semigroup Compactifications of Semidirect Products

Abstract

Abstract.Let S and T be semigroups, S(r)T a semidirect product, and F a C*-algebra of bounded, complex-valued functions on S(?)T. Necessary and sufficient conditions are given for the /•'-compactification of S(t) T to be expressible as a semidirect product of compactifications of S and T. This result is used to show that the strongly almost periodic compactification of S (7) T is a semidirect product and that, in certain general cases, the analogous statement holds for the almost periodic compactification and the left uniformly continuous compactification of S@ T. Applications are made to wreath products.