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Primitive idempotent measures on compact semigroups

Published online by Cambridge University Press:  20 January 2009

J. Duncan
J. Duncan
Affiliation:
King's College, University of Aberdeen
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Let S be a compact semigroup (with jointly continuous multiplication) and let P(S) denote the probability measures on S, i.e. the positive regular Borel measures on S with total mass one. Then P(S) is a compact semigroup with convolution multiplication and the weak* topology. Let II(P(S)) denote the set of primitive (or minimal) idempotents in P(S). Collins (2) and Pym (5) respectively have given complete descriptions of II(P(S)) when S is a group and when K(S), the kernel of S, is not a group. Choy (1) has given some characterizations of II(P(S)) for the general case. In this paper we present some detailed and intrinsic characterizations of II((P(S)) for various classes of compact semigroups that are not covered by the results of Collins and Pym.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 1 , June 1970 , pp. 95 - 103
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

REFERENCES

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(5) Pym, J. S., Idempotent measures on semigroups, Pacific J. Math. 12 (1962), 685–698.CrossRefGoogle Scholar