A generalization of Gudder-Nagy's theorem with numerical ranges of operators
A generalization of Gudder-Nagy's theorem with numerical ranges of operators
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DOI：
10.1063/1.3544484
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发表时间：
2011-02
影响因子：
1.3
通讯作者：
H. Du;Yan-Ni Dou;Hai-Yan Zhang;L. Shen
中科院分区：
文献类型：
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作者：
H. Du;Yan-Ni Dou;Hai-Yan Zhang;L. Shen
本文证明了对于可分复Hilbert空间H上的有界线性算子A，B，C，对所有x∈H且∥x∥=1，(Ax，x)(Bx，x)=(Cx，x)，当且仅当存在复数c∈C，使得A=Ci且C=Cb或B=Ci且C=CA.
In this paper, we prove that, for A, B, C, which are bounded linear operators on a separable complex Hilbert space H, (Ax, x)(Bx, x) = (Cx, x) for all x∈H with ∥x∥ = 1, if and only if there exists a complex number c∈C, such that A = cI and C = cB or B = cI and C = cA.