The exact cardinality of the set of topological left invariant means on an amenable locally compact group
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- by Anthony To Ming Lau and Alan L. T. Paterson PDF
- Proc. Amer. Math. Soc. 98 (1986), 75-80 Request permission
Abstract:
The purpose of this note is to prove that if $G$ is an amenable locally compact noncompact group, then the set of topological left invariant means on ${L_\infty }(G)$ has cardinality ${2^{{2^d}}}$, where $d$ is the smallest cardinality of the covering of $G$ by compact sets. We also prove that in this case the spectrum of the bounded left uniformly continuous complex-valued functions contains exactly ${2^{{2^d}}}$ minimal closed invariant subsets (or left ideals)References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 75-80
- MSC: Primary 43A07; Secondary 43A15
- DOI: https://doi.org/10.1090/S0002-9939-1986-0848879-6
- MathSciNet review: 848879