Quadratic identity and real ternary derivations

چکیده مقاله

We consider a mapping D from a unital C*-algebra A, containing a distinguished tern, into its iterated dual spaces, A^(n) which satisfies the quadratic identity (neither linearity nor continuity is assumed). In the first step we prove that D is additive, and by assuming continuity we conclude that D is a real ternary derivation.