Ternary derivable mappings on involutive Banach algebras

Abstract

In this note we prove that a continuous linear mapping from a unital C$^*$-algebra $A$ into its dual space $A^*$ is a ternary derivation whenever it is ternary derivable at the unit of $A$. This is an improvement of the result which shows that any continuous linear mapping on a unital C$^*$-algebra $A$ which is ternary derivable at the unit of $A$, is a ternary derivation.