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CHARACTERIZATIONS OF STRICTLY SINGULAR AND STRICTLY COSINGULAR OPERATORS BY PERTURBATION CLASSES

Published online by Cambridge University Press:  02 August 2011

PIETRO AIENA ,
MANUEL GONZÁLEZ  and
ANTONIO MARTÍNEZ-ABEJÓN
PIETRO AIENA
Affiliation:
Dipartimento di Metodi e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy E-mail: paiena@unipa.it
MANUEL GONZÁLEZ
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander, Spain E-mail: gonzalem@unican.es
ANTONIO MARTÍNEZ-ABEJÓN
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, E-33007 Oviedo, Spain E-mail: ama@uniovi.es
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Abstract

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We consider a class of operators that contains the strictly singular operators and it is contained in the perturbation class of the upper semi-Fredholm operators PΦ+. We show that this class is strictly contained in PΦ+, solving a question of Friedman. We obtain similar results for the strictly cosingular operators and the perturbation class of the lower semi-Fredholm operators PΦ−. We also characterize in terms of PΦ+ and in terms of PΦ−. As a consequence, we show that and are the biggest operator ideals contained in PΦ+ and PΦ−, respectively.

Keywords

47A53
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 1 , January 2012 , pp. 87 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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