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perturbations of self-adjoint operators in semifinite von Neumann algebras

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讲座题目:perturbations of self-adjoint operators in semifinite von Neumann algebras
讲座人: 沈隽皓 教授
讲座时间:15:00
讲座日期:2018.06.13
地点:数学与信息科学学院学术交流厅

讲座内容简介:

Extending Weyl-von Neumann Theorem on perturbation of self-adjoint operators, in 1979 Voiculescu was able to show that a normal operator in B(H) is a diagonal operator plus an arbitrary small Hilbert-Schmitz operator where H is a separable Hilbert space. On the other hand, the classical Kato-Rosenblum theorem states that the absolute continuous part of a self-adjoint operator in B(H) can't be changed, relative to unitary equivalence, by a perturbation of a trace class operator.

Assume that M is a properly infinite separable von Neumann algebra with a faithful normal semifinite tracial weight (an easy example of such M is B(H) with a canonical trace).  In the first half of the talk, we will prove that a normal operator in a separable seminifinite von Neumann algebra is a diagonal operator plus an arbitrary small max(\|.\|, \|.\|_2)-perturbation in M. We will devote our second half of the talk to show that, if H is the real part of a non-normal hyponormal operator in M, then H can't be a diagonal operator plus a trace class operator in M.

讲座人简介:

沈隽皓,美国新罕布什尔大学数学与统计学院终身教授。沈隽皓教授于2004年毕业于美国宾夕法尼亚大学,师从著名算子理论与算子代数专家Richard Kadison。毕业后任职于美国新罕布什尔大学,长期从事泛函分析,算子理论与算子代数的研究工作,研究成果卓著, 在《Journal of Functional Analysis》,《Transactions of the American Mathematical Society》,《Journal of Operator Theory》,《Canadian Journal of Mathematics》,《The Bulletin of the London Mathematical Society》,《Integral Equations and Operator Theory》等数学名刊上发表论文30余篇。

 

 
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