The range of a derivation on a Jordan-Banach algebra (Q2717714)

I. M. Singer and J. Wermer proved in 1955 that a continuous derivation on a commutative Banach algebra has the range in the (Jacobson) radical of the algebra, and 30 years later M. P. Thomas showed that the continuity assumption is redundant. The noncommutative Singer-Wermer conjecture, whether a (not necessarily continuous) derivation on a Banach algebra leaves primitive ideals invariant, remains still open.NEWLINENEWLINENEWLINETo discuss a Jordan analogon to the noncommutative Singer-Wermer conjecture is the aim of the present paper. Thus, in Theorem 5.4, it is proved that the Singer-Wermer conjecture for Jordan-Banach algebras is equivalent to some statements, which, as a whole, could be summarized by saying that a derivation of a Jordan-Banach algebra whose range satisfies certain associative relations modulo the radical has actually the range into the radical. A similar result for Banach algebras, where commutative relations replace associative ones, is stated in Theorem 5.5.