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ON THE PERTURBATION CLASSES OF CONTINUOUS SEMI-FREDHOLM OPERATORS

Published online by Cambridge University Press:  01 May 2003

PIETRO AIENA ,
MANUEL GONZÁLEZ  and
ANTONIO MARTINÓN
PIETRO AIENA
Affiliation:
Dipartimento di Matematica, Universià di Palermo, 90128 Palermo, Italia e-mail: paiena@unipa.it
MANUEL GONZÁLEZ
Affiliation:
Departamento de Matemáticas, Universidad de Cantabria, 39071 Santander, Spain e-mail: gonzalem@unican.es
ANTONIO MARTINÓN
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain e-mail: anmarce@ull.es
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Abstract

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We prove that the perturbation class of the upper semi-Fredholm operators from $X$ into $Y$ is the class of the strictly singular operators, whenever $X$ is separable and $Y$ contains a complemented copy of $C[0, 1]$. We also prove that the perturbation class of the lower semi-Fredholm operators from $X$ into $Y$ is the class of the strictly cosingular operators, whenever $X$ contains a complemented copy of $\ell_1$ and $Y$ is separable. We can remove the separability requirements by taking suitable spaces instead of $C[0, 1]$ or $\ell_1$.

Keywords

47A5347A55
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 45 , Issue 1 , January 2003 , pp. 91 - 95
Copyright
2003 Glasgow Mathematical Journal Trust

Footnotes

The first-named author was supported by the M.U.R.S.T. (Italy), Fondi ex 40.The second-named author was supported by the DGES (Spain), Grant PB 97-1489.The third-named author was supported by the Gobierno de Canarias (Spain), PI2001/039.