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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Syndetic sets and amenability

Author: Vern I. Paulsen
Journal: Proc. Amer. Math. Soc. 140 (2012), 1997-2001
MSC (2010): Primary 43A07; Secondary 22A15
Published electronically: September 30, 2011
MathSciNet review: 2888187
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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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Vern I. Paulsen
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3476

PII: S 0002-9939(2011)11247-4
Received by editor(s): February 2, 2011
Published electronically: September 30, 2011
Additional Notes: This research was supported in part by NSF grant DMS-0600191.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.