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Properties of certain measures on a topological group

Published online by Cambridge University Press:  24 October 2008

S. W. Drury
S. W. Drury
Affiliation:
University of Cambridge
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Extract

We denote by M(G) the space of bounded regular borel measures on a non-discrete locally compact Abelian topological group G. Under the convolution product and norm of total mass M(G) becomes a complex commutative banach algebra. We denote by Φ the space of m.l.f.s (multiplicative linear functionals) on M(G) and by σ the subset of Φ consisting of functionals symmetric in the sense that

where * denotes the usual involution on M(G). These matters are discussed more fully in Williamson (1).

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 1011 - 1013
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Williamson, J. H.Proc. Edinburgh Math. Soc. 11 (1959), 195.CrossRefGoogle Scholar
(2)Williamson, J. H.Proceedings of the Tulane University Symposium on Function Algebras (1965), p. 186; Scott Foresman and Co.Google Scholar
(3)Williamson, J. H.Proceedings of the 5th Matscience Symposium (to appear).Google Scholar
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(5)Gelfand, I. M., Raikov, D. A. and Šilov, G. E.Commutative normed rings. Chelsea.CrossRefGoogle Scholar