On generalized derivations in Banach algebras

Volume 194 / 2009

Nadia Boudi, Said Ouchrif Studia Mathematica 194 (2009), 81-89 MSC: 47B47, 47B48. DOI: 10.4064/sm194-1-5

Abstract

We study generalized derivations $G$ defined on a complex Banach algebra $A$ such that the spectrum $\sigma (Gx)$ is finite for all $x \in A$. In particular, we show that if $A$ is unital and semisimple, then $G$ is inner and implemented by elements of the socle of $A$.

Authors

  • Nadia BoudiDépartement de Mathématiques
    Faculté des Sciences
    Université My Ismail
    Zitoune Meknes, Maroc
    e-mail
  • Said OuchrifDépartement de Mathématiques
    Faculté des Sciences
    Université My Ismail
    Zitoune Meknes, Maroc
    e-mail

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