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Orderings in locally compact Abelian groups and the theorem of F. and M. Riesz

Published online by Cambridge University Press:  24 October 2008

Edwin Hewitt  and
Shozo Koshi
Edwin Hewitt
Affiliation:
The University of Washington, Seattle W A 98195, USA
Shozo Koshi
Affiliation:
University of Hokkaido, Sapporo 060, Japan
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Extract

Background (1·1). Ordered Abelian groups have been studied for nearly a century. Since the early 1950's, it has been recognized that orderings in locally compact Abelian groups can play an important rôle in harmonic analysis on such groups. In this paper we study orderings, especially in topological Abelian groups with either topological or measure-theoretic properties, obtaining nearly a complete classification of such orderings. We then apply these results to determine the limitations of the celebrated theorem of F. and M. Riesz on such groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 3 , May 1983 , pp. 441 - 457
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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