Proyecciones
Vol. 23, No 2, pp. 111-121, August 2004.
Universidad Catolica del Norte
Antofagasta - Chile

ON AUTOMATIC SURJECTIVITY OF SOME ADDITIVE TRANSFORMATIONS

MUSTPHA ECH-CHÉRIF EL KETTANI
EL HOUCINE El BOUCHIBTI

Universidad de Fes, Maroc

Received : May 2003. Accepted : May 2004.

correspondencia a:

Abstract

Let X be an infinite dimensional Banach space and let Φ: B(X) → B(X) be a spectrum preserving additive transformation. We show that if the image of quasi-nilpotent operators contains all quasi-nilpotent operators, then Φ is an automophism or an antiautomorphism of B(X).

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Mustapha Ech-chérif El Kettani
Département de Math et Informatique
Faculté des sciences Dhar El Mehraz
B.P 1796 Atlas Fès Maroc
e-mail : melkettani@caramail.com

El Houcine El Bouchibti
Département de Math et Informatique
Faculté des sciences Dhar El Mehraz
B.P 1796 Atlas Fès Maroc
e-mail : elbouchibti@hotmail.com