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Transactions of the American Mathematical Society

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Extreme invariant means without minimal support


Author: Lonnie Fairchild
Journal: Trans. Amer. Math. Soc. 172 (1972), 83-93
MSC: Primary 43A07; Secondary 28A70
DOI: https://doi.org/10.1090/S0002-9947-1972-0308685-2
MathSciNet review: 0308685
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Abstract: Let $ S$ be a left amenable semigroup. We show that if $ S$ has a subset satisfying a certain condition, then there is an extreme left invariant mean on $ S$ whose support is not a minimal closed invariant subset of $ \beta S$. Then we show that all infinite solvable groups and countably infinite locally finite groups have such subsets.


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  • [1] C. Chou, Minimal sets and ergodic measures for $ \beta N\backslash N$, Illinois J. Math. 13 (1969), 777-788. MR 40 #2814. MR 0249569 (40:2814)
  • [2] M. M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509-544. MR 19, 1067. MR 0092128 (19:1067c)
  • [3] L. Gillman and M. Jerison, Rings of continuous functions, University Series in Higher Math., Van Nostrand, Princeton, N. J., 1960. MR 22 #6994. MR 0116199 (22:6994)
  • [4] W. H. Gottschalk and G. A. Hedlund, Topological dynamics, Amer. Math. Soc. Colloq. Publ., vol. 36, Amer. Math. Soc., Providence, R. I., 1955. MR 17, 650. MR 0074810 (17:650e)
  • [5] A. Lau, Topological semigroups with invariant means in the convex hull of the multiplicative means, Trans. Amer. Math. Soc. 148 (1970), 69-84. MR 41 #1911. MR 0257260 (41:1911)
  • [6] T. Mitchell, Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc. 119 (1965), 244-261. MR 33 #1743. MR 0193523 (33:1743)
  • [7] R. R. Phelps, Lectures on Choquet's theorem, Van Nostrand, Princeton, N. J., 1966. MR 33 #1690. MR 0193470 (33:1690)
  • [8] C. Wilde, On amenable semigroups and applications of the Stone-Čech compactification, Thesis, University of Illinois, Urbana, Ill., 1964.
  • [9] C. Wilde and K. Witz, Invariant means and the Stone-Čech compactification, Pacific J. Math 21 (1967), 577-586. MR 35 #3423. MR 0212552 (35:3423)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0308685-2
Keywords: Amenable semigroup, extreme point, Stone-Čech compactification, minimal invariant set
Article copyright: © Copyright 1972 American Mathematical Society

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