Derivations mapping into the socle, III

Volume 197 / 2010

Nadia Boudi, Peter Šemrl Studia Mathematica 197 (2010), 141-155 MSC: Primary 47B47. DOI: 10.4064/sm197-2-2


Let $A$ be a Banach algebra, and let $d: A \to A$ be a continuous derivation such that each element in the range of $d$ has a finite spectrum. In a series of papers it has been proved that such a derivation is an inner derivation implemented by an element from the socle modulo the radical of $A$ (a precise formulation of this statement can be found in the Introduction). The aim of this paper is twofold: we extend this result to the case where $d$ is not necessarily continuous, and we give a complete description of such maps in the semisimple case.


  • Nadia BoudiDépartement de Mathématiques
    Université Moulay Ismail
    Faculté des Sciences, BP 11201
    Zitoune, Meknes, Morocco
  • Peter ŠemrlFaculty of Mathematics and Physics
    University of Ljubljana
    Jadranska 19, SI-1000 Ljubljana, Slovenia

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