A generalization of Gudder-Nagy's theorem with numerical ranges of operators

作者：Du, Hong-Ke^*; Dou, Yan-Ni; Zhang, Hai-Yan; Shen, Ling-Min

来源：Journal of Mathematical Physics, 2011, 52(2): 023501.

DOI：10.1063/1.3544484

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 is an element of H with parallel to x parallel to = 1, if and only if there exists a complex number c is an element of C, such that A = cI and C = cB or B = cI and C = cA.

• 出版日期2011-2
• 单位陕西师范大学