Duality results for perturbation classes of semi-Fredholm operators
type: Item
instance of: scholarly article
title: Duality results for perturbation classes of semi-Fredholm operators
zbMATH Open document ID: 1237.47012
published in: Archiv der Mathematik
publication date: 2011-12-13T00:00:00Z
review text: The summary perfectly describes this paper: ``The perturbation classes problem for semi-Fredholm operators asks when the equalities \(\mathcal{SS}(X,Y)=P\Phi_+(X,Y)\) and \(\mathcal{SC}(X,Y)=P\Phi _-(X,Y)\) are satisfied, where \(\mathcal{SS}\) and \(\mathcal{SC}\) denote the strictly singular and the strictly cosingular operators, and \(P\Phi _+\) and \(P\Phi _-\) denote the perturbation classes for upper semi-Fredholm and lower semi-Fredholm operators. We show that, when \(Y\) is a reflexive Banach space, \(\mathcal{SS}(X^*,Y^*)=P\Phi_+(X^*,Y^*)\) if and only if \(\mathcal{SC}(X,Y)=P\Phi _-(X,Y)\), and \(\mathcal{SC}(X^*,Y^*)=P\Phi _-(X^*,Y^*)\) if and only if \(\mathcal{SS}(X,Y)=P\Phi_+(X,Y)\). Moreover, we give examples showing that both direct implications fail in general.''
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 5988048
zbMATH Keywords: strictly singular operator
zbMATH Keywords: semi-Fredholm operator
zbMATH Keywords: perturbation class
author: M. González
reviewed by: Dorota Gabor
MaRDI profile type: Publication
full work available at URL: s00013-011-0313-7
OpenAlex ID: W2027361192
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DOI: 10.1007/S00013-011-0313-7
description: scientific article; zbMATH DE number 5988048