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Wigner’s theorem and L^2-isometry on projection lattices

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报告人:  王利广 教授

讲座日期:2020-12-07

讲座时间:15:00

报告地点: Tencent会议 (会议 ID438 767 510

主办单位: 数学与信息科学学院

讲座人概况:

王利广,曲阜师范大学教授,博士生导师。20057月于中国科学院获理学博士学位。研究方向为泛函分析和算子代数。目前正在主持国家自然科学基金面上项目一项,主持山东省自然科学基金面上项目一项;已主持完成国家自然科学基金面上项目和数学天元基金各一项、山东省自然科学基金面上项目一项。已在J. Functional Analysis》、《J. Operator Theory等期刊发表论文20余篇。

讲座概况:

Wigners theorem shows that every transition probability preserving surjection on the set of all rank one projections on a Hilbert space is induced by a unitary or an antiunitary. Wigners theorem can be interpreted as a result of mappings that preserves certain metric on the set of projections. Recently, Geh\{e}r and \u{S}emrl have characterized the general form of surjective isometries of the set of all projections on an infinite-dimensional separable Hilbert space using unitaries and antiunitaries. In this talk, we will study the surjective $L^2$-isometries of the projection lattice of an infinite dimensional Hilbert space and show that every such isometry can also be described by unitaries and antiunitaries. This talk is based on joint work with Wenming Wu and Wei Yuan.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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