The exposed points of the set of invariant means
Author:
Tianxuan Miao
Journal:
Trans. Amer. Math. Soc. 347 (1995), 14011408
MSC:
Primary 43A07
DOI:
https://doi.org/10.1090/S00029947199512601742
MathSciNet review:
1260174
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Abstract  References  Similar Articles  Additional Information
Abstract: Let $G$ be a $\sigma$compact infinite locally compact group, and let $LIM$ be the set of left invariant means on ${L^\infty }(G)$. We prove in this paper that if $G$ is amenable as a discrete group, then $LIM$ has no exposed points. We also give another proof of the Granirer theorem that the set $LIM(X,G)$ of $G$invariant means on ${L^\infty }(X,\beta ,p)$ has no exposed points, where $G$ is an amenable countable group acting ergodically as measurepreserving transformations on a nonatomic probability space $(X,\beta ,p)$.

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Additional Information
Keywords:
Locally compact groups,
amenable groups,
invariant means,
the exposed points
Article copyright:
© Copyright 1995
American Mathematical Society