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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On topologically invariant means on a locally compact group

Author: Ching Chou
Journal: Trans. Amer. Math. Soc. 151 (1970), 443-456
MSC: Primary 22.65
MathSciNet review: 0269780
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Abstract: Let $\mathcal {M}$ be the set of all probability measures on $\beta N$. Let G be a locally compact, noncompact, amenable group. Then there is a one-one affine mapping of $\mathcal {M}$ into the set of all left invariant means on ${L^\infty }(G)$. Note that $\mathcal {M}$ is a very big set. If we further assume G to be $\sigma$-compact, then we have a better result: The set $\mathcal {M}$ can be embedded affinely into the set of two-sided topologically invariant means on ${L^\infty }(G)$. We also give a structure theorem for the set of all topologically left invariant means when G is $\sigma$-compact.

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Keywords: Locally compact group, amenable group, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-compact group, invariant mean, topological invariant mean, Stone-&#268;ech compactification of <I>N</I>, affine homeomorphism
Article copyright: © Copyright 1970 American Mathematical Society