The perturbation classes problem for subprojective and superprojective Banach spaces

Manuel González; Javier Pello; Margot Salas-Brown

doi:10.1016/j.jmaa.2020.124191

The perturbation classes problem for subprojective and superprojective Banach spaces

Manuel González, Javier Pello, Margot Salas-Brown

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Abstract

We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when X is subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y.

Original language	English (US)
Article number	124191
Journal	Journal of Mathematical Analysis and Applications
Volume	489
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2020.124191
State	Published - Sep 15 2020

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.jmaa.2020.124191

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title = "The perturbation classes problem for subprojective and superprojective Banach spaces",

abstract = "We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when X is subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y.",

author = "Manuel Gonz{\'a}lez and Javier Pello and Margot Salas-Brown",

note = "Funding Information: Supported in part by MICINN (Spain) Grant MTM2016-76958. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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AU - Pello, Javier

AU - Salas-Brown, Margot

PY - 2020/9/15

Y1 - 2020/9/15

N2 - We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when X is subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y.

AB - We show that the perturbation class for the upper semi-Fredholm operators between two Banach spaces X and Y coincides with the strictly singular operators when X is subprojective and that the perturbation class for the lower semi-Fredholm operators coincides with the strictly cosingular operators when Y is superprojective. Similar results were previously obtained under stronger conditions for X and Y.

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The perturbation classes problem for subprojective and superprojective Banach spaces

Abstract

All Science Journal Classification (ASJC) codes

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