Geodesic
Superdiagonal forms for completely continuous linear operators
Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 163-170

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Koros, Demetrios. Superdiagonal forms for completely continuous linear operators. Glasgow mathematical journal, Tome 23 (1982) no. 2, pp. 163-170. doi: 10.1017/S0017089500004936
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[1] 1.Altman, M., On linear functional equations in locally convex linear topological spaces, Studia Math. 13 (1953), 194–207. Google Scholar | DOI

[2] 2.Altman, M., Invariant subspaces of completely continuous operators in locally convex topological spaces, Studia Math. 15 (1956), 129–130. Google Scholar | DOI

[3] 3.Ringrose, J. R., Superdiagonal forms for compact linear operators, Proc. London Math. Soc. (3) 12 (1962), 367–384. Google Scholar | DOI

[4] 4.Robertson, A. P. and Robertson, W. J., Topological vector spaces (Cambridge University Press, 1964). Google Scholar

[5] 5.Treves, F., Topological vector spaces, distributions and kernels (Academic Press, 1967). Google Scholar

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