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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
Published electronically: September 30, 2011
MathSciNet review: 2888187
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Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. S. Burns, The existence of disjoint smallest ideals in the two natural products on $ \beta S$, Semigroup Forum 63 (2001), no. 2, 191-201. MR 1830683 (2002d:22003)
  • 2. M.M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509-544. MR 0092128 (19:1067c)
  • 3. E. Granirer and Anthony T. Lau, Invariant means on locally compact groups, Illinois J. Math. 15 (1971), 249-257. MR 0277667 (43:3400)
  • 4. Neil Hindman and Dona Strauss, Algebra in the Stone-Cech Compactification, de Gruyter Expositions in Mathematics, Volume 27, Walter de Gruyter, New York, 1998. MR 1642231 (99j:54001)
  • 5. T. Mitchell, Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc. 119 (1965), 244-261. MR 0193523 (33:1743)

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Additional Information

Vern I. Paulsen
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3476

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.

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