设P(H)表示维数大于2的复Hilbert空间H上的所有正交投影.S(H)是H上的自伴算子代数.得到满射Ф:S(H)→S(H)满足A—λB∈P(H)←→Ф(A)-λФ(B)∈P(H)当且仅当存在酉算子或共轭酉算子U:H→H,使得对任意A∈S(H),有Ф(A)=UAU^*.
Let P(H) be the set of all orthogonal projections on a complex Hilbert space H with dim H 〉 2. S(H) is a self-adjoint operator algebra on H. It is shown that a surjective map Ф:S(H)→S(H) satisfies A-λB∈P(H)←→Ф(A)-λФ(B)∈P(H) if and only if there is a unitary operator or a conjugate unitary operator U:H→H such that Ф(A)=UAU^* for all A∈S(H).