Derivations mapping into the socle, III

Nadia Boudi, and Peter Šemrl. "Derivations mapping into the socle, III." Studia Mathematica 197.2 (2010): 141-155. <http://eudml.org/doc/285826>.

@article{NadiaBoudi2010,
abstract = {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.},
author = {Nadia Boudi, Peter Šemrl},
journal = {Studia Mathematica},
keywords = {derivations; semisimple Banach algebras; socle; finite spectrum},
language = {eng},
number = {2},
pages = {141-155},
title = {Derivations mapping into the socle, III},
url = {http://eudml.org/doc/285826},
volume = {197},
year = {2010},
}

TY - JOUR
AU - Nadia Boudi
AU - Peter Šemrl
TI - Derivations mapping into the socle, III
JO - Studia Mathematica
PY - 2010
VL - 197
IS - 2
SP - 141
EP - 155
AB - 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.
LA - eng
KW - derivations; semisimple Banach algebras; socle; finite spectrum
UR - http://eudml.org/doc/285826
ER -