Perturbations of self-adjoint operators in semifinite von Neumann algebras: Kato-Rosenblum theorem
Perturbations of self-adjoint operators in semifinite von Neumann algebras: Kato-Rosenblum theorem
复制标题
半有限冯诺依曼代数中自伴算子的扰动：Kato-Rosenblum 定理
DOI：
10.1016/j.jfa.2018.04.006
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发表时间：
2018
影响因子：
1.7
通讯作者：
Wang Liguang
中科院分区：
文献类型：
--
作者：
李启慧;Shen Junhao;Shi Rui;Wang Liguang
In the paper, we prove an analogue of the Kato–Rosenblum theorem in a semifinite von Neumann algebra. Let M be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space H and let τ be a faithful normal semifinite tracial weight of M. Suppose that H and H 1 are self-adjoint operators affiliated with M. We show that if H− H 1 is in M∩ L 1 (M, τ), then the norm absolutely continuous parts of H and H 1 are unitarily equivalent. This implies that the real part of a non-normal hyponormal operator in M is not a perturbation by M∩ L 1 (M, τ) of a diagonal operator.
