Almost Homomorphisms Between Unital $C^*$-Algebras: A Fixed Point Approach

Abstract

Let A, B be two unital C * −algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h : A −→ B which satisfies h(2 n uy) = h(2 n u)h(y) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, ···, is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of * −homomorphisms on unital C * −algebras.