English

Syndetic Sets and Amenability

Functional Analysis 2011-02-03 v2 Operator Algebras

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.

Keywords

Cite

@article{arxiv.1002.3157,
  title  = {Syndetic Sets and Amenability},
  author = {Vern I. Paulsen},
  journal= {arXiv preprint arXiv:1002.3157},
  year   = {2011}
}
R2 v1 2026-06-21T14:47:40.094Z