Abstract
AbstractLet 𝒜 and ℬ be two primeC*-algebras. In this paper, we investigate the additivity of map Φ from 𝒜 onto ℬ that are bijective unital and satisfiesΦ(AP+λPA∗)=Φ(A)Φ(P)+λΦ(P)Φ(A)∗,$$\Phi(AP+\lambda PA^{*})=\Phi(A)\Phi(P)+\lambda \Phi(P)\Phi(A)^{*}, $$for allA∊ 𝒜 andP∊ {P1,I𝒜−P1} whereP1is a nontrivial projection in 𝒜 andλ∊ {−1, +1}. Then, Φ is *-additive.
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