Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22.65

Retrieve articles in all journals with MSC: 22.65

Additional Information

Keywords: Locally compact group, amenable group, $ \sigma $-compact group, invariant mean, topological invariant mean, Stone-Čech compactification of N, affine homeomorphism
Article copyright: © Copyright 1970 American Mathematical Society