Additivity of maps preserving productsAP±PA*onC*-algebras

Abstract Let 𝒜 and ℬ be two prime C * -algebras. In this paper, we investigate the additivity of map Φ from 𝒜 onto ℬ that are bijective unital and satisfies Φ (AP+λPA∗) =Φ (A) Φ (P) +λΦ (P) Φ (A) ∗, (AP+ PA^*) = (A) (P) + (P) (A) ^*, for all A ∊ 𝒜 and P ∊ P 1, I 𝒜 − P 1 where P 1 is a nontrivial projection in 𝒜 and λ ∊ −1, +1. Then, Φ is *-additive.