On automatic surjectivity of some additive transformations

Mustapha Ech-chérif El Kettani, El Houcine El Bouchibti

Resumen


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).

Palabras clave


Banach spaces; additive transformations; quasi-nilpotent operators; automorphisms; antiautomorphism; espacios de Banach; operadores cuasi nilpotentes; automorfismos; antiautomorfismos; transformaciones aditivas.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172004000200004

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