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Semi-simple locally compact monothetic semi-algebras

Published online by Cambridge University Press:  20 January 2009

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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Bonsall and Tomiuk have shown, in (3), the connection between the local compactness of a monothetic semi-algebra and the spectral properties of a generating element. This theme was developed, in (4), to give a complete characterisation of prime, strict locally compact monothetic semi-algebras in terms of the spectrum of a generator (Theorem A). Here we extend this result to the case of a semi-simple locally compact monothetic semi-algebra (Theorem B).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 3 , June 1969 , pp. 215 - 219
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1)Albert, A. A.Structure of Algebras (Amer. Math. Soc. Colloquium Publication vol. XXIV, New York, 1939).Google Scholar
(2)Bonsall, F. F.Locally compact semi-algebras, Proc. London Math. Soc. (3) 13 (1963), 51–70.Google Scholar
(3)Bonsall, F. F. and Tomiuk, B. J.The semi-algebra generated by a compact linear operator, Proc. Edinburgh Math. Soc. (2) 14 (1965), 177–196.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