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), 7580
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 complexvalued functions contains exactly minimal closed invariant subsets (or left ideals)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198608488796
PII:
S 00029939(1986)08488796
Keywords:
Amenable locally compact groups,
invariant means,
left thick subsets,
uniformly continuous functions,
minimal invariant sets
Article copyright:
© Copyright 1986
American Mathematical Society
