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Perturbation theory for a linear operator

Published online by Cambridge University Press:  24 October 2008

J. H. Webb
Affiliation:
Gonville and Caius College, Cambridge

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
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Goldberg, S.Linear operators and their conjugates. Pacific J. Math. 9 (1959), 6979.CrossRefGoogle Scholar
(2)Goldberg, S.Ranges and inverses of perturbed linear operators. Pacific J. Math. 9 (1959), 701706.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), 273322.CrossRefGoogle Scholar
(5)Phillips, R. S.The adjoint semi-group. Pacific J. Math. 5 (1955), 269282.CrossRefGoogle Scholar
(6)Taylor, A. E.Introduction to functional analysis. (John Wiley and Sons, Inc. 1958.)Google Scholar