On the Cauchy-Rassias stability of the Trif functional equation in C*-algebras

Let A, B be two unital C*-algebras, and let q := k(n - 1)/(n - k) for given integers k, n with 2 less than or equal to k less than or equal to n - 1. Consider an almost unital approximately linear mapping h :A --> B. We prove that h is a homomorphism when h(q(-j) xu) = h(x)h(q(-j) u) for all x is an element of A, all unitaries u is an element of A, and all sufficiently large integers j. Moreover, when A has real rank zero, we give conditions in order for h to be a *-homomorphism. Furthermore, we investigate the Cauchy-Rassias stability of the Trif functional equation associated with *-homomorphisms between unital C*-algebras and *-derivations of a unital C*-algebra. (C) 2004 Elsevier Inc. All rights reserved.