Syndetic sets and amenability

Author:

Paulsen Vern

Abstract

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference5 articles.

1. The existence of disjoint smallest ideals in the two natural products on 𝛽𝑆;Burns, Shea D.;Semigroup Forum,2001

2. Amenable semigroups;Day, Mahlon M.;Illinois J. Math.,1957

3. Invariant means on locally compact groups;Granirer, E.;Illinois J. Math.,1971

4. De Gruyter Expositions in Mathematics;Hindman, Neil,1998

5. Constant functions and left invariant means on semigroups;Mitchell, Theodore;Trans. Amer. Math. Soc.,1965

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