On automatic surjectivity of some additive transformations
Author
Ech-chérif El Kettani, Mustapha
El Bouchibti, El Houcine
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).