On *-homomorphisms between JC*-algebras

Abstract

It is shown that every almost unital almost linear mapping f : A --> B of JC*-algebra A to a JC*-algebra B is a homomorphism when f (2(n)u o y) = f (2(n)u) o f (y) holds for all unitaries u is an element of A, all y is an element of A, and all n = 0, 1, 2,..., and that every almost unital almost linear continuous mapping f : A --> B of a JC*-algebra A of real rank zero to a JC*-algebra B is a homomorphism when f(2(n)uoy) = f(2(n)u) o f(y) holds for all u is an element of {v is an element of A vertical bar v = v*, parallel to v parallel to = 1, v is invertiblel, all y is an element of A, and all n = 0, 1, 2,.... Furthermore, we are going to prove the generalized Hyers-Ulam-Rassias stability of *-homomorphisms between JC*-algebras, and C-linear *-derivations on JC*-algebras.