ON AUTOMATIC SURJECTIVITY OF SOME ADDITIVE TRANSFORMATIONS
Author
EL KETTANI,MUSTPHA ECH-CHÉRIF
El BOUCHIBTI,EL HOUCINE
Abstract
Let X be an infinite dimensional Banach space and let <FONT FACE=Symbol>Ö</FONT>: 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 <FONT FACE=Symbol>Ö</FONT> is an automophism or an antiautomorphism of B(X)