LetAand B be two unital C∗-algebras. It is shown that if a surjectivemap : A → B satisfies: A∗B + B∗A 2 = (A) ∗ (B) + (B) ∗ (A) 2 for every A, B ∈ A, and if is injective or (−I ) = −I , then is the direct sum of two ∗-homomorphisms, one of which is C-linear and the other is conjugate C-linear.
