Means, homomorphisms, and compactifications of weighted semitopological semigroups

We consider some almost periodic type function algebras on a weighted semitopological semigroup, and using the set of multiplicative means on each of these algebras, we define their corresponding weighted semigroup compactifications. This will constitute an effective tool for investigating the properties of the function algebras concerned. We also show that these compactifications do not retain all the nice properties of the ordinary semigroup compactifications unless we impose some restrictions on the weight functions.