Multipliers or the space of almost-convergent functions on a semigroup

Let 5 be a countably infinite left amenable cancellative semigroup, FL(S) the space of left almost-convergent functions on S. The purpose of this paper is to show that the following two statements concerning a bounded real function ƒ on S are equivalent:(i)'formula presented'(ii)there is a constant a such that for each e>0 there exists a set 'formula presented' satisfying (a) 'formula presented' for each left invariant mean 'formula presented' and (b) 'formula presented' if 'formula presented'.