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Certain semigroups embeddabable in topological groups

Part of: Abstract harmonic analysis Topological and differentiable algebraic systems

Published online by Cambridge University Press:  09 April 2009

Heneri A. M. Dzinotyiweyi
Heneri A. M. Dzinotyiweyi
Affiliation:
Department of Mathematics University of ZimbabweP. O. Box MP 167 Mount Pleasant, Salisbury, Zimbabwe
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Abstract

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In this paper we study commutative topological semigroups S admitting an absolutely continuous measure. When S is cancellative we show that S admits a weaker topology J with respect to which (S, J) is embeddable as a subsemigroup with non-empty interior in some locally compact topological group. As a consequence, we deduce certain results related to the existence of invariant measures on S and for a large class of locally compact topological semigroups S, we associate S with some useful topological subsemigroup of a locally compact group.

MSC classification

Secondary: 22A20: Analysis on topological semigroups 43A05: Measures on groups and semigroups, etc.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 1 , August 1982 , pp. 30 - 39
Copyright
Copyright © Australian Mathematical Society 1982

References

Baker, A. C. and Baker, J. W. (1970), ‘Algebras of measures on a locally compact semigroup II’, J. London Math. Soc. 2, 651–659.CrossRefGoogle Scholar
Baker, A. C. and Baker, J. W. (1972), ‘Algebras of measures on a locally compact semigroup III’, J. London Math. Soc. 4, 685–695.CrossRefGoogle Scholar
Dzinotyiweyi, H. A. M. (1978a), ‘Algebras of measures on C-distinguished topological semigroups’, Math. Proc. Cambridge Philos. Soc. 84, 323–336.CrossRefGoogle Scholar
Dzinotyiweyi, H. A. M. (1978b), ‘On the analogue of the group algebra for locally compact semigroups’, J. London Math. Soc. 17, 489–506.CrossRefGoogle Scholar
Dzinotyiweyi, H. A. M. and Sleijpen, G. L. G. (1979), ‘A note on measures on foundation semigroups with weakly compact orbits’, Pacific J. Math. 81, 61–69.CrossRefGoogle Scholar
Ellis, R. (1957), ‘Locally compact transformation groups’, Duke Math. J. 24, 119–125.CrossRefGoogle Scholar
Kelley, J. L. (1955), General topology (Van Nostrand, Princeton, N.J.).Google Scholar
Paalman-de-Miranda, A. B. (1970), Topological semigroups (Mathematical centre tracts, Amsterdam).Google Scholar
Paterson, A. L. T. (1977), ‘Invariant measure semigroups’, Proc. London Math. Soc. 35, 313–332.CrossRefGoogle Scholar
Rigelhoff, R. (1971), ‘Invariant measures on locally compact semigroups’, Proc. Amer. Math. Soc. 28, 173–176.CrossRefGoogle Scholar
Rothman, N. J. (1960), ‘Embedding of topological semigroups’, Math. Ann. 139. 197–203.CrossRefGoogle Scholar
Sleijpen, G. L. G. (1976), Convolution measure algebras on semigroups (Thesis, Katholieke Universiteit, Toernooiveld, Nijmegen).Google Scholar
Sleijpen, G. L. G. (1978), ‘Locally compact semigroups and continuous translation of measures’, Proc. London Math. Soc. 37, 75–97.CrossRefGoogle Scholar
Willard, S. (1970), General topology (Addison-Wesley, Reading, Mass.).Google Scholar