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On the instability of non-semi-Fredholm closed operators under compact perturbations with applications to ordinary differential operators

Published online by Cambridge University Press:  14 November 2011

L. E. Labuschagne
L. E. Labuschagne
Affiliation:
Department of Mathematics, University of Cape Town, Rondebosch 7700, Cape Town, Republic of South Africa
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Synopsis

The stability of several natural subsets of the bounded non-semi-Fredholm operators undercompact perturbations were studied by R. Bouldin [2] in separable Hilbert spaces and by M. Gonzales and V. M. Onieva [6] in Banach spaces. The aim of this paper is to study this problem for closed operators in operator ranges. The main results are a characterisation of the non-semi-Fredholm operators with respect to α-closed and α-compact operators as well as a generalisation of a result of M. Goldman [5]. We also give some applications of the theory developed to ordinary differential operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 1-2 , 1988 , pp. 97 - 108
Copyright
Copyright © Royal Society of Edinburgh 1988

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