Slowly oscillating functions in semigroup compactifications and convolution algebras (Q996264)

The notion of slowly oscillating functions is extended in the paper under review to any non-compact locally compact group, and developed to be more suitable in the uncountable or non-\(\sigma\)-compact case. These newly defined slowly oscillating functions yield in a natural manner a common method of proof to various key theorems in the areas of semigroup compactifications and Banach algebras related to a locally compact group with a type of convolution as product. In addition to this method being the most natural and simple, it also leads to a generalization of some of the results and to the achievement of some new results. Several of these results concern the topological centres of convolution algebras and semigroup compactifications.