Let A be a Banach algebra, and let d: A → 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-2-2,
author = {Nadia Boudi and Peter \v Semrl},
title = {Derivations mapping into the socle, III},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {141-155},
zbl = {1210.47057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-2-2}
}
Nadia Boudi; Peter Šemrl. Derivations mapping into the socle, III. Studia Mathematica, Tome 196 (2010) pp. 141-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm197-2-2/