Geodesic
Superdiagonal forms for related linear operators
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 19-23

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The concept of superdiagonal forms for n × nmatrices T with complex entries has been extended by J. R. Ringrose [4] to the setting of compact linear operators T:X→X acting on a complex Banach space X. In a recent paper D. Koros [2] generalized Ringrose's approach to the case of compact linear operators T:X→X on a complex locally convex space X. The reason why both authors confine their attention to the class of compact linear operators is that the existence of proper closed invariant subspaces is, aside from Riesz-Schauder theory, the main tool in their construction. In the present paper it is shown that the existence of superdiagonal forms possesses a certain permanence property in the following sense. 
Wrobel, Volker. Superdiagonal forms for related linear operators. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 19-23. doi: 10.1017/S0017089500005723
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[2] 2.Koros, D., Superdiagonal forms for completely continuous linear operators, Glasgow, Math. J. 23 (1982), 163–170. Google Scholar | DOI

[3] 3.Pietsch, A., Operator ideals (Berlin, 1978). Google Scholar

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

[5] 5.Wrobel, V., Spektraltheorie beschränkter linearer Operatoren, Math. Nachr. 80 (1977), 151–156. Google Scholar | DOI

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