A characterisation of dual space valued ternary derivations on C*-algebras

Abstract

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 identity T({a,b,a})={T(a),b,a}+{a,T(b),a}+{a,b,T(a)} for every a,b in A, is additive and consequently a ternary derivation.