Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-28T14:38:36.566Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuity of the generalized kernel and range of semi-Fredholm operators

Published online by Cambridge University Press:  04 October 2011

M. Ó Searcóid  and
T. T. West
M. Ó Searcóid
Affiliation:
University College, Dublin
T. T. West
Affiliation:
Trinity College, Dublin
Get access Rights & Permissions [Opens in a new window]

Extract

Let X denote a Banach space over the complex field ℂ and let B(X) be the Banach algebra of all bounded linear operators on X. If T ε B(X), we write n(T) = dim ker (T) and d(T) = codim T(X). Suppose that Y is a subspace invariant under T; then TY will denote the restriction of T to Y and Y the operator on X/Y defined by

Y: x/Y →(Tx)/Y

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 513 - 522
Copyright
Copyright © Cambridge Philosophical Society 1989

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

[1] Aupetit, B. and Zemánek, J.. Uniformly regular families of commuting operators. (To appear.)Google Scholar
[2] Goldman, M. A. and Kračkovskiǐ, S. N.. Invariance of certain subspaces associated with the operator A — λI (Russian). Dokl. Akad. Nauk SSSR 154 (1964), 500–502.Google Scholar
[3] Homer, R. H.. Regular extensions and the solvability of operator equations. Proc. Amer. Math. Soc. 12 (1961), 415–418.CrossRefGoogle Scholar
[4] Kaashoek, M. A.. Stability theorems for closed linear operators. Indag. Math. 27 (1965), 452–466.CrossRefGoogle Scholar
[5] Kato, T.. Perturbation Theory for Linear Operators (Springer-Verlag, 1966).Google Scholar
[6] Livčak, A. Ja. Operators with finite-dimensional salient of zeros on the Riesz kernel: duality and non-commuting perturbations (Russian). VINITI, Voronezh (1983) RZh Mat. 6B (1983), 692.Google Scholar
[7] Saphar, P.. Contributions à l'étude des applications linéaires dans un espace de Banach. Bull. Soc. Math. France 92 (1964), 363–384.CrossRefGoogle Scholar
[8] West, T. T.. A Riesz-Schauder theorem for semi-Fredholm operators. Proc. Roy. Irish Acad. Sect. A 87 (1987), 137–146.Google Scholar