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The Range of Invariant Means on Locally Compact Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Roy C. Snell
Roy C. Snell*
Affiliation:
Department of National Defence, Royal Roads Military College, FMO, Victoria, B.C.
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Abstract

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It has been shown by E. Granirer that for certain infinite amenable discrete groups G there exists a nested family of left almost convergent subsets of G on which every left invariant mean on m(G) attains as its range the entire [0,1] interval. This paper examines the range of left invariant means on L∞(G) for infinite locally compact abelian groups G and demonstrates the existence in every such group of a nested family of left almost convergent Borel subsets on which every left invariant mean on L∞ (G) attains as its range the interval [0,1],

Keywords

43A0728A70
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 567 - 573
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Granirer, E., On the range of an invariant mean Trans. Amer. Math. Soc. 125 (1966), 384-394.Google Scholar
2. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis I, Springer-Verlag (1963).Google Scholar
3. Reiter, H., Classical Harmonic Analysis and Locally Compact Groups, Oxford Press (1968).Google Scholar
4. Snell, R., The range of invariant means on locally compact groups and semigroups, Proc. Amer. Math. Soc. 37(1973), 441-447.Google Scholar
5. Lindenstraus, J., A short proof of Liapounoff's Convexity Theorem, J. of Math, and Mech. 15 (1966), 971-972.Google Scholar
6. Wong, J., Topologically Stationary Locally Compact Groups and Amenability, Trans. Amer. Math. Soc. 144 (1969) 351-363.Google Scholar