Conjugate linear maps from C*-algebras into their dual spaces which are ternary derivable at the unit element

Abstract

We prove that every continuous conjugate linear mapping from a unital C*-algebra A into its dual space, A*, which is ternary derivable at the unit element of A is a ternary derivation. This is somehow a ternary counterpart result for (binary) derivations on associative algebras which proves that any linear continuous map from a unital C*-algebra A into a Banach A-bimodule which is derivable at the unit element of A, is a derivation.