Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T07:34:09.698Z Has data issue: false hasContentIssue false
  • English
  • Français

Unilateral quasi-regularizers of closed operators

Published online by Cambridge University Press:  24 October 2008

R. W. Cross
R. W. Cross
Affiliation:
University of Cape Town
Get access Rights & Permissions [Opens in a new window]

Extract

Let X and Y be normed spaces and let L(X, Y) denote the set of linear transformations from X into Y, with domain D(T) and range R(T). For a given T ∈ L(X, Y) we investigate the existence and properties of a closed densely defined operator S ∈ L(Y, X) such that ST − I/D(T) (or TS − I/D(S)) is a bounded operator of finite dimensional range. These results were previously announced without proof in (2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 3 , May 1980 , pp. 471 - 480
Copyright
Copyright © Cambridge Philosophical Society 1980

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)Cross, R. W.Quasi-complementation and the existence of unilateral inverses of closed operators. Notices of the South African Math. Soc. 9 (1977), 75.Google Scholar
(2)Cross, R. W.Quasi-regularizers of closed operators. Math. Colloq. Univ. Cape Town, 11 (1977), 145–154.Google Scholar
(3)Cross, R. W.On the continuous linear image of a Banach space. J. Australian Math. Soc. (to appear).Google Scholar
(4)Goldberg, S.Unbounded linear operators (New York, McGraw-Hill, 1966).Google Scholar
(5)Jameson, G. J. O.Topology and normed spaces (London, Chapman & Hall, 1974).Google Scholar
(6)Lin, C-S.Regularizes of closed operators. Canad. Math. Bull. 17 (1974), 67–71.Google Scholar
(7)Lindenstrauss, J.On subspaces of Banach spaces without quasi-complements. Israel J. Math. 6 (1968), 36–38.CrossRefGoogle Scholar
(8)Nashed, M. Z. and Votruba, G. F.A unified approach to generalized inverses of linear operators. Bull. Amer. Math. Soc. 80 (1974), 825–835.Google Scholar
(9)Nieto, J. I.On Fredholm Operators and the essential spectrum of singular integral operators. Math. Ann. 178 (1968), 62–77.Google Scholar
(10)Vladimirskiǐ, Ju. N.Strictly cosingular operators. Soviet Math. Dokl. 8 (1967), 739–740.Google Scholar