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.
Cite
@article{arxiv.1002.3157,
title = {Syndetic Sets and Amenability},
author = {Vern I. Paulsen},
journal= {arXiv preprint arXiv:1002.3157},
year = {2011}
}