Syndetic sets and amenability

Paulsen, Vern

doi:10.1090/S0002-9939-2011-11247-4

Syndetic sets and amenability
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by Vern I. Paulsen

Proc. Amer. Math. Soc. 140 (2012), 1997-2001

DOI: https://doi.org/10.1090/S0002-9939-2011-11247-4

Published electronically: September 30, 2011

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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.

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