Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-11T01:37:02.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Perturbation theory for a linear operator

Published online by Cambridge University Press:  24 October 2008

J. H. Webb
J. H. Webb
Affiliation:
Gonville and Caius College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

We extend certain results of the theory of closed operators in Banach spaces to general linear operators in normed spaces. A ‘state diagram’ for linear operators is drawn up. We prove some perturbation theorems, improving or correcting certain results of Goldberg.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 11 - 20
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Goldberg, S.Linear operators and their conjugates. Pacific J. Math. 9 (1959), 69–79.CrossRefGoogle Scholar
(2)Goldberg, S.Ranges and inverses of perturbed linear operators. Pacific J. Math. 9 (1959), 701–706.CrossRefGoogle Scholar
(3)Kaashoek, M. A. Closed linear operators on Banach spaces. Thesis, Leiden University, 1963.Google Scholar
(4)Kato, T.Perturbation theory for nullity, deficiency and other quantities of linear operators. J. Analyse Math. 6 (1958), 273–322.CrossRefGoogle Scholar
(5)Phillips, R. S.The adjoint semi-group. Pacific J. Math. 5 (1955), 269–282.CrossRefGoogle Scholar
(6)Taylor, A. E.Introduction to functional analysis. (John Wiley and Sons, Inc. 1958.)Google Scholar