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On the operators which are invertible modulo an operator ideal

Published online by Cambridge University Press:  17 April 2009

Pietro Aiena ,
Manuel González  and
Antonio Martínez-Abejón
Pietro Aiena
Affiliation:
Dipartimento di Matematica ed Applicazioni, Università di Palermo, Viale delle Scienze, I-90128 Palermo, Italy
Manuel González
Affiliation:
Departamento de Matemáticas, Universidad de Oviedo, E-33007 Oviedo, Spain
Antonio Martínez-Abejón
Affiliation:
Departamento de Matemáticas, Universidad de Cantabria, E-39071 Santander, Spain
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We study the semigroups l and r of left and right invertible operators modulo an operator ideal , respectively. We show that these semigroups allow us to obtain useful characterisations of the radical rad of  For example, rad; is the perturbation class for l and r.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 233 - 243
Copyright
Copyright © Australian Mathematical Society 2001

References

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