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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Operators which have a closed quasi-nilpotent part


Authors: Pietro Aiena, Maria Luisa Colasante and Manuel González
Journal: Proc. Amer. Math. Soc. 130 (2002), 2701-2710
MSC (2000): Primary 47A10, 47A11; Secondary 47A53, 47A55
Published electronically: March 12, 2002
MathSciNet review: 1900878
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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.


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Additional Information

Pietro Aiena
Affiliation: Dipartimento di Matematica ed Applicazioni, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
Email: paiena@mbox.unipa.it

Maria Luisa Colasante
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Los Andes, Merida, Venezuela
Email: marucola@ciens.ula.ve

Manuel González
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, Santander, Spain
Email: gonzalem@ccaix3.unican.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06386-4
PII: S 0002-9939(02)06386-4
Keywords: Quasi-nilpotent part, single valued extension property, operators with a generalized Kato decomposition
Received by editor(s): December 8, 2000
Received by editor(s) in revised form: April 20, 2001
Published electronically: March 12, 2002
Additional Notes: The research of the first two authors was supported by the International Cooperation Project between the University of Palermo (Italy) and Conicit-Venezuela
The research of the third author was supported by DGICYT, Spain
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society