CHARACTERIZING JORDAN MAPS ON C*-ALGEBRAS THROUGH ZERO PRODUCTS

Let A and B be C*-algebras, let X be an essential Banach A-bimodule and let T : A -> B and S : A -> X be continuous linear maps with T surjective. Suppose that T(a) T(b)+ T(b) T(a) = 0 and S(a) b + bS(a) + aS(b) + S(b) a = 0 whenever a, b is an element of A are such that ab = ba = 0. We prove that then T = w Phi and S = D+Psi, where w lies in the centre of the multiplier algebra of B, Phi: A -> B is a Jordan epimorphism, D: A -> X is a derivation and Psi : A -> X is a bimodule homomorphism.