Title: Characterizing Jordan maps on <i>C</i>*-algebras through zero products
Abstract:Abstract 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...Abstract 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 ε A are such that ab = ba = 0. We prove that then T = w Φ and S = D + Ψ, where w lies in the centre of the multiplier algebra of B , Φ: A → B is a Jordan epimorphism, D: A → X is a derivation and Ψ: A → X is a bimodule homomorphism.Read More