Title: Additive mappings on C ∗ -algebras sub-preserving absolute values of products
Abstract:Let be a -algebra of real rank zero and be a -algebra with unit I. It is shown that if is an additive mapping which satisfies for every and for some with , then the restriction of mapping ϕ to is a Jo...Let be a -algebra of real rank zero and be a -algebra with unit I. It is shown that if is an additive mapping which satisfies for every and for some with , then the restriction of mapping ϕ to is a Jordan homomorphism, where denotes the set of all self-adjoint elements. We will also show that if ϕ is surjective preserving the product and an absolute value, then ϕ is a -linear or -antilinear ∗-homomorphism on . MSC:47B49, 46L05, 47L30.Read More