Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T06:27:21.366Z Has data issue: false hasContentIssue false
  • English
  • Français

Superdiagonal forms for related linear operators

Published online by Cambridge University Press:  18 May 2009

Volker Wrobel
Volker Wrobel
Affiliation:
Mathematisches Seminar, der Universität Klel, Olshausenstrabe 40, D-2300 Kiel 1, Fed. Rep., Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 19 - 23
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Enflo, P., On the invariant subspace problem in Banach spaces, Séeminaire Maurey-Schwartz (1975–1976). Espaces Lp Applications Radonifiantes et Géeometrie des Espaces de Banach, Exp. No. 14–15, Centre Math., École Polytech., (Palaiseau, 1976).Google Scholar
2.Koros, D., Superdiagonal forms for completely continuous linear operators, Glasgow, Math. J. 23 (1982), 163–170.CrossRefGoogle Scholar
3.Pietsch, A., Operator ideals (Berlin, 1978).Google Scholar
4.Ringrose, J. R., Superdiagonal forms for compact linear operators, Proc. London Math. Soc. (3) 12 (1962), 367–384.CrossRefGoogle Scholar
5.Wrobel, V., Spektraltheorie beschränkter linearer Operatoren, Math. Nachr. 80 (1977), 151–156.CrossRefGoogle Scholar