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Abstract harmonic analysis of generalised functions on locally compact semigroups with applications to invariant means

Published online by Cambridge University Press:  09 April 2009

James C. S. Wong
James C. S. Wong
Affiliation:
Department of Mathematics and Statistics, The University of Calgary, Canada, T2N IN4.
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Abstract

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Let S be a locally compact semigroup and M(S) its measure algebra. It is shown that the dual M(S)* is isometrically order isomorphic to the space GL(S) of all generalised functions on S first introduced by Šreǐder (1950). Moreover, convolutions of elements in each of the spaces M(S)* and GL(S) can be defined in such a way that the above isomorphism preserves convolutions. These results on representation of functionals in M(S)* by generalised functions practically open up a new chapter in abstract harmonic analysis. As an example, some applications to invariant means on locally compact semigroups are given.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 84 - 94
Copyright
Copyright © Australian Mathematical Society 1977

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