The questions when a derivation on a Jordan-Banach algebra has quasi-nilpotent values, and when it has the range in the radical, are discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-2-4, author = {M. Bre\v sar and A. R. Villena}, title = {The range of a derivation on a Jordan-Banach algebra}, journal = {Studia Mathematica}, volume = {147}, year = {2001}, pages = {177-200}, zbl = {0982.46034}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-2-4} }
M. Brešar; A. R. Villena. The range of a derivation on a Jordan-Banach algebra. Studia Mathematica, Tome 147 (2001) pp. 177-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-2-4/