The exact cardinality of the set of topological left invariant means on an amenable locally compact group

Authors:
Anthony To Ming Lau and Alan L. T. Paterson

Journal:
Proc. Amer. Math. Soc. **98** (1986), 75-80

MSC:
Primary 43A07; Secondary 43A15

MathSciNet review:
848879

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Abstract: The purpose of this note is to prove that if is an amenable locally compact noncompact group, then the set of topological left invariant means on has cardinality , where is the smallest cardinality of the covering of by compact sets. We also prove that in this case the spectrum of the bounded left uniformly continuous complex-valued functions contains exactly minimal closed invariant subsets (or left ideals)

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DOI:
https://doi.org/10.1090/S0002-9939-1986-0848879-6

Keywords:
Amenable locally compact groups,
invariant means,
left thick subsets,
uniformly continuous functions,
minimal invariant sets

Article copyright:
© Copyright 1986
American Mathematical Society