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Let B(H) be the algebra of all bounded linear operators on a Hilbert space H with dim(H) ＞ 2. Let GP(H) be the subset of B(H) of all generalized projection operators. In this paper, we give a complete characterization of surjective maps Φ : B(H) → B(H) satisfying A−λB ∈ GP(H) ⇔ Φ(A) − λΦ(B) ∈ GP(H) for any A, B ∈ B(H) and λ ∈ C.

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