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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Extreme invariant means without minimal support

Author: Lonnie Fairchild
Journal: Trans. Amer. Math. Soc. 172 (1972), 83-93
MSC: Primary 43A07; Secondary 28A70
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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PII: S 0002-9947(1972)0308685-2
Keywords: Amenable semigroup, extreme point, Stone-Čech compactification, minimal invariant set
Article copyright: © Copyright 1972 American Mathematical Society