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Superdiagonal forms for completely continuous linear operators

Published online by Cambridge University Press:  18 May 2009

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
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

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