Characterization of jordan*-derivations by local action on rings with involution

Let R be a ring with an involution ∗ and a symmetric idempotent e. It is shown that, under some mild conditions on R, an additive map δ : R → R satisfies δ(ab + ba) = δ(a)b ∗ + aδ(b) + δ(b)a ∗ + bδ(a) whenever ab = e for a, b ∈ R if and only if δ is a Jordan *-derivation.

Keywords:

Rings with involution , Jordan *-derivations , Derivations