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Superdiagonal forms for completely continuous linear operators

Published online by Cambridge University Press:  18 May 2009

Demetrios Koros
Demetrios Koros
Affiliation:
17 Akti Koyntoyrioti, Kastella, Piraeus, Greece
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Altman [1] showed that Riesz-Schauder theory remains valid for a completely continuous linear operator on a locally convex Hausdorflf topological vector space over the complex field. In a later paper [2], he proved an analogue of the Aronszajn-Smith result; specifically, he showed that such an operator possesses a proper closed invariant subspace. The purpose of this paper is to show that Ringrose's theory of superdiagonal forms for compact linear operators [3] can be generalized to the case of a completely continuous linear operator on a locally convex Hausdorff topological vector space over the complex field. However, the proof given in [3] requires considerable modification.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 163 - 170
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Altman, M., On linear functional equations in locally convex linear topological spaces, Studia Math. 13 (1953), 194–207.CrossRefGoogle Scholar
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3.Ringrose, J. R., Superdiagonal forms for compact linear operators, Proc. London Math. Soc. (3) 12 (1962), 367–384.CrossRefGoogle Scholar
4.Robertson, A. P. and Robertson, W. J., Topological vector spaces (Cambridge University Press, 1964).Google Scholar
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