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The Semi-Algebra Generated by a Compact Linear Operator

Published online by Cambridge University Press:  20 January 2009

F. F. Bonsall  and
B. J. Tomiuk
B. J. Tomiuk
Affiliation:
The University, Newcastle upon Tyne
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We prove that if t is a compact linear operator that is not quasi-nilpotent and is appropriately normalised, then the closed semi-algebra A(t) generated by t is locally compact. The theory of locally compact semi-algebras (2) is therefore applicable to A(t), and we show that it can be used to obtain spectral properties of t.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 3 , June 1965 , pp. 177 - 196
Copyright
Copyright Edinburgh Mathematical Society 1965

References

REFERENCES

(1) Birkhoff, G. and Maclane, S., A Survey of modern algebra, (New York, 1953).Google Scholar
(2) Bonsall, F. F., Locally compact semi-algebras, Proc. London Math. Soc. (3) 13 (1963) 5170.CrossRefGoogle Scholar
(3) Bonsall, F. F., On the representation of cones and semi-algebras with given generators, to appear in Proc. London Math. Soc.Google Scholar
(4) Gantmacher, F. R., Applications of the theory of matrices (New York, 1959).Google Scholar
(5) Klee, V. L. Jr., Separation properties of convex cones, Proc. American Math. Soc., 6 (1955) 313318.CrossRefGoogle Scholar
(6) Krein, M. G. and Rutman, M. A., Linear operators leaving invariant a cone in a Banach space, Uspehi Mat. Nauk (N.S.) 3, No. 1 (23), (1948) 395.Google Scholar
Also American Math. Soc. Translations, Series 1, 10 (1962).Google Scholar
(7) Namioka, I., Partially ordered linear topological spaces, American Math. Soc. Memoir, 24 (1957).Google Scholar
(8) Numakura, K., On bicompact semigroups, Math. J. Okayama Univ., 1 (1952) 99108.Google Scholar
(9) Wielandt, H., Unzerlegbare, nicht negative matrizen, Math. Z., 52 (1950) 642648.CrossRefGoogle Scholar