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Syndetic sets and amenability
Author:
Vern I. Paulsen
Journal:
Proc. Amer. Math. Soc. 140 (2012), 1997-2001
MSC (2010):
Primary 43A07; Secondary 22A15
Posted:
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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Additional Information
Vern I. Paulsen
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email:
vern@math.uh.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-11247-4
PII:
S 0002-9939(2011)11247-4
Received by editor(s):
February 2, 2011
Posted:
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 after
28 years from publication.
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