a characterisation of dual space valued ternary derivations on c*-algebras

In this note we prove that a homogenous mapping t (neither additivity nor continuity is assumed a priori) from a unital c*-algebra a into its dual space, a*, which satisfies the following identityt({a, b, a}) = {t(a), b, a} + {a, t(b), a} + {a, b, t(a)}for every a, b a, is additive and consequently a ternary derivation.