A note on skew Jordan triple derivations on ∗-rings

Abstract

Let [Formula: see text] be a [Formula: see text]-torsion free unital ∗-ring containing nontrivial symmetric idempotent. In this article, it is shown that if a map [Formula: see text] : [Formula: see text] (not necessarily additive) satisfies [Formula: see text] for all [Formula: see text], then [Formula: see text] is additive. Moreover, if [Formula: see text] is self-adjoint, then [Formula: see text] is a ∗-derivation. As an applications, we apply our main result to some special classes of unital ∗-rings and ∗-algebras such as prime ∗-ring, prime ∗-algebra, standard operator algebra, factor von Neumann algebra and von Neumann algebra with no central summands of type [Formula: see text].