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A contribution to the solution of the compact correction problem for operators on a Banach space

Published online by Cambridge University Press:  18 May 2009

Mícheál Ó Searcóid
Mícheál Ó Searcóid
Affiliation:
Roinn na Matamaitice, Coláiste na Hollscoile, Baile Átha Cliath 4, Éire.
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We consider the hypothesis that an operator T on a given Banach space can always be perturbed by a compact operator K in such a way that, whenever a complex number A is in the semi-Fredholm region of T + K, then T + K – λ is either bounded below or surjective. The hypothesis has its origin in the work of West [11], who proved it for Riesz operators on Hilbert space. In this paper, we reduce the general Banach space problem to one of considering only operators of a special type, operators which are, in a spectral sense, natural generalizations of the Riesz operators studied by West.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 2 , May 1989 , pp. 219 - 229
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

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