We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-1-5,
author = {Nadia Boudi and Said Ouchrif},
title = {On generalized derivations in Banach algebras},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {81-89},
zbl = {1181.47035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-1-5}
}
Nadia Boudi; Said Ouchrif. On generalized derivations in Banach algebras. Studia Mathematica, Tome 192 (2009) pp. 81-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-1-5/