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Amenability and Substantial Semigroups

Published online by Cambridge University Press:  20 November 2018

James C. S. Wong
James C. S. Wong*
Affiliation:
Department of Mathematics, Statistics & Computing Science, University of Calgary, Calgary, Alberta
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Abstract

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In this paper, we introduce the concept of topological left substantial subsemigroup of a locally compact semigroup S and prove that if T is such a subsemigroup in S and M(T) is the measure algebra of T, then M(T)* is topological left amenable iff M(S)* is topological left amenable, an extension of a similar result for discrete semigroups.

Keywords

22.0522.242.542.56Locally compact semigroupsMeasure algebrasTopological left invariant meansLeft substantial semigroupsLeft ideals
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 231 - 234
Copyright
Copyright © Canadian Mathematical Society 1976

Footnotes

(1)

Research supported by the National Research Council of Canada Grant No. A8227.

References

1. Day, M., Amenable semigroups, Illinois J. Math., 1 (1957), 509–544.10.1215/ijm/1255380675CrossRefGoogle Scholar
2. Greenleaf, F. P., Invariant Means on Topological Groups, Van Nostrand Math. Studies, 1969.Google Scholar
3. Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis I, Springer-Verlag, 1963.Google Scholar
4. Kelley, J., General Topology, Van Nostrand, New York, 1968.Google Scholar
5. Mitchell, T., Constant functions and left invariant means on semigroups, Trans. Amer. Math. Soc, 119 (1965), 244–261.10.1090/S0002-9947-1965-0193523-8CrossRefGoogle Scholar
6. Wong, James C. S., An ergodic property of locally compact amenable semigroups, Pacific J. Math. 48 (1973) 615–619.10.2140/pjm.1973.48.615CrossRefGoogle Scholar
7. Wong, James C. S., Absolutely continuous measures on locally compact semigroups, Canadian Math. Bull. 18 (1), 1975.10.4153/CMB-1975-023-3CrossRefGoogle Scholar
8. Wong, James C. S., A characterization of locally compact amenable semigroups, to appear.Google Scholar
9. Wong, James C. S., A characterization of topological left thick subsets in locally compact left amenable semigroups, to appear.10.2140/pjm.1976.62.295CrossRefGoogle Scholar