Decomposition theorem for weak almost periodic functions

Abstract

Let S be a group and a topological semigroup. It is proved that a continuous complex weak almost periodic function on S can be represented uniquely as a sum of a continuous almost periodic function and a continuous weak almost periodic function such that the weak closure of its orbit contains zero. The proof depends mainly on the weak almost periodic compactfication. To obtain this compactification, we use topological concepts like Ruppert (Compact semitopological semigroup: an intrinsic theory. 1984, Springer Verlag) rather than the operator theoretic techniques of Deleeuw and Glicksberg (Acta Math., 1961, lOS, 63-97).