Homomorphisms and derivations in C^*-algebras

Abstract

Using the Hyers-Ulam-Rassias stability method of functional equations, we investigate homomorphisms in $C^*$-algebras and Lie $C^*$-algebras, and derivations on $C^*$-algebras and Lie $C^*$-algebras associated with the following functional equation \begin{eqnarray*} \frac{1}{q} f(qx+qy+qz) = f(x)+f(y)+f(z) \end{eqnarray*} for a fixed nonzero rational number $q$.