Let B(X ) be the algebra of all bounded linear operators on a complex Banach space X with dim X ≥ 3. We characterize the forms of a bijective map φ : B(X ) → B(X ) which satisfies φ(A.B ◦ A) = φ(A).φ(B) ◦ φ(A), for every A, B ∈ B(X ), where ’.’ is the usual product and ”◦” is Jordan product.
