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Compact semigroups in commutative Banach algebras

Published online by Cambridge University Press:  24 October 2008

M. A. Kaashoek  and
T. T. West
M. A. Kaashoek
Affiliation:
Free University, Amsterdam; Trinity College, Dublin
T. T. West
Affiliation:
Free University, Amsterdam; Trinity College, Dublin
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Extract

A monothetic semigroup is a topological semigroup with jointly continuous multiplication which contains a dense cyclic subsemigroup. These semi-groups arise in a natural way in the study of semi-algebras. In (4) we showed that a compact monothetic semigroup in a Banach algebra can be characterized in terms of the spectral properties of a generating element. In this paper these spectral theorems are linked with the well-known structure theory of compact semigroups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 265 - 274
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Austin, C. W.Duality theorems for commutative semigroups. Trans. Amer. Math. Soc. 109 (1963), 245–256.CrossRefGoogle Scholar
(2)Hewitt, E.Compact monothetic semigroups. Duke Math. J. 23 (1956), 447–457.CrossRefGoogle Scholar
(3)Hewitt, E. and Ross, K. A.Abstract harmonic analysis. Vol. I (Berlin, 1963).Google Scholar
(4)Kaashoek, M. A. and West, T. T.Locally compact monothetic semi-algebras. Proc. London Math. Soc. (3) 18 (1968), 428–438.CrossRefGoogle Scholar
(5)Paalman-de Miranda, A. B.Topological semigroups (Amsterdam, 1964).Google Scholar
(6)Williamson, J. H.Harmonic analysis on semigroups. J. London Math. Soc. 42 (1967), 1–41.CrossRefGoogle Scholar