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- 2015
B(H)上中心化子的一个局部特征
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Abstract:
摘要： 设H是实数域或复数域F上的Hilbert空间, Ф:B(H)→B(H)是一个线性映射。本文证明了如果 2Ф(P)=PФ(P)+Ф(P)P对任意幂等算子P∈B(H)成立, 则存在λ∈F使得对任意A∈B(H), 有Ф(A)=λA。
Abstract: Let H be a Hilbert space over the real or complex field F. Suppose Ф:B(H)→B(H) is a linear map such that 2Ф(P)=PФ(P)+Ф(P)P holds for all idempotent operators P∈B(H), then there exists a λ∈F such that Ф(A)=λA for all A∈B(H)
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