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Operators which have a closed quasi-nilpotent part |
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| Authors: | Pietro Aiena Maria Luisa Colasante Manuel Gonzá lez |
| Affiliation: | Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy ; Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Merida, Venezuela ; Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, Santander, Spain |
| Abstract: | We find several conditions for the quasi-nilpotent part of a bounded operator acting on a Banach space to be closed. Most of these conditions are established for semi-Fredholm operators or, more generally, for operators which admit a generalized Kato decomposition. For these operators the property of having a closed quasi-nilpotent part is related to the so-called single valued extension property. |
| Keywords: | Quasi-nilpotent part single valued extension property operators with a generalized Kato decomposition |
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