Approximation of linear mappings in Banach modules over C*-algebras

Abstract

Let X, Y be Banach modules over a C*-algebra and let r(1), ..., r(n). R be given. Using fixed-point methods, we prove the stability of the following functional equation in Banach modules over a unital C*-algebra: Sigma(n)(j=1) f(1/2 Sigma(1 <= i <= n,i not equal j) r(i)x(i) - 1/2r(j)x(j)) + Sigma(n)(i=1) r(i)f(x(i)) = nf(1/2 Sigma(n)(i=1) r(i)x(i)). As an application, we investigate homomorphisms in unital C*-algebras.