Two classes of operators related to the perturbation classes problem

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URI: https://hdl.handle.net/10902/32432
ISSN: 2538-225X
ISSN: 2662-2009
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Autoría
González Ortiz, ManuelAutoridad Unican; Salas-Brown, Margot
Fecha
2023-07
Derechos
This article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense,which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
Publicado en
Advances in Operator Theory, 2023, 8(3), 41
Editorial
Springer
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Palabras clave
Perturbation classes problem
Semi-Fredholm operator
Strictly singular operator
Resumen/Abstract
Let SS and SC be the strictly singular and the strictly cosingular operators acting between Banach spaces, and let PΦ+ and PΦ+ be the perturbation classes for the upper and the lower semi-Fredholm operators. We study two classes of operators ΦS and ΦC that satisfy SS ⊂ ΦS ⊂ PΦ+ and SC ⊂ ΦC ⊂ PΦ_. We give some conditions under which these inclusions become equalities, from whichwe derive some positive solutions to the perturbation classes problem for semi-Fredholm operators.
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This article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense,which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.Excepto si se señala otra cosa, la licencia del ítem se describe como This article is licensed under a CreativeCommonsAttribution 4.0 InternationalLicense,which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.