  We prove that if an infinite, discrete semigroup has the property that every
right syndetic set is left syndetic, then the semigroup has a left invariant
mean. We prove that the weak*-closed convex hull of the two-sided translates of
every bounded function on an infinite discrete semigroup contains a constant
function. Our proofs use the algebraic properties of the Stone-Cech
compactification.

Functional Analysis;Operator Algebras