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Operators which have a closed quasi-nilpotent part
Author(s):
Pietro
Aiena;
Maria
Luisa
Colasante;
Manuel
González
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2701-2710.
MSC (2000):
Primary 47A10, 47A11;
Secondary 47A53, 47A55
Posted:
March 12, 2002
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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:
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
Posted:
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
Copyright of article:
Copyright
2002,
American Mathematical Society
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