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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
2.Altman, M., Invariant subspaces of completely continuous operators in locally convex topological spaces, Studia Math. 15 (1956), 129–130.CrossRefGoogle Scholar
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
5.Treves, F., Topological vector spaces, distributions and kernels (Academic Press, 1967).Google Scholar