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数学与信息科学学院系列学术报告(一)

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报告人: 许庆祥教授、邓春源教授

讲座日期:2020-11-02

讲座时间:14:40

报告地点:Tencent会议(935 822 979

主办单位:数学与信息科学学院

 

报告题目一:Generalized parallel sum of adjointable operators on Hilbert C*-modules

报告人: 许庆祥教授

讲座时间:14:40

报告人概况:

许庆祥, 上海师范大学数理学院教授、博士生导师。19851989年本科就读于浙江师范大学数学系,1989年至1995年研究生就读于复旦大学数学研究所,师从严绍宗教授和陈晓漫教授。1995年到上海师范大学数学系工作至今。

近年来主要从事算子理论和矩阵方面的研究工作,被MathSinNet收录文章69, 部分文章发表于SIAM J. Numer. Anal., SIAM J. Matrix Anal. Appl., J. London Math. Soc., J. Operator TheoryLinear Algebra Appl.等期刊上. 目前担任期刊Advances in Operator TheoryFacta Universitatis, Series: Mathematics and Informatics的编委。

报告概况:

We introduce the notion of a tractable pair of operators as well as that of the generalized parallel sum in the setting of adjointable operators on Hilbert C^*-modules. Some significant results about the parallel sum known for matrices and Hilbert space operators are extended to the case of the generalized parallel sum. In particular, a factorization theorem on the parallel sum is proved, and a common upper bound of two positive operators is constructed in the Hilbert C*-module case. The harmonic mean for positive operators on Hilbert C*-modules is also dealt with. This is a joint work with C. Fu, M.S. Moslehian and A. Zamani.

 

报告题目二:On the parallel addition and subtraction of operators on a Hilbert space

报告人: 邓春源教授

讲座时间:16:00

报告人概况:

 邓春源,华南师范大学教授、博士生导师。20002006年就读于网赌官方正规平台数学与信息科学学院,师从杜鸿科教授,先后获理学硕士学位和理学博士学位。20067月至今在华南师范大学工作,先后任讲师(2006)、副教授(2007)、教授(2011),博导(2014)。在此期间,从20129月到20139月在美国威廉玛丽学院进行学术访问。主要从事算子理论与算子代数方面的研究工作,在算子矩阵理论、幂等算子理论、算子的广义逆理论等方面取得了一系列研究成果。主持或参加多项省部级自然科学基金,已在国内外刊物上发表论文70余篇。

报告概况:

We extend the operations of parallel addition A:B and parallel subtraction A\div B from the cone of bounded nonnegative self-adjoint operators to the linear bounded operators on a Hilbert space. The basic properties of the parallel addition and subtraction were developed for nonnegative matrices in finite-dimensional spaces.However, without suitable restrictions, very little of the preceding theories will hold for bounded linear operators A and B acting in Hilbert space. 

In this talk, generalization to non-selfadjoint operators is considered  and various properties of parallel addition and subtraction are given. The common upper and lower bounds of positive operators by using the parallel sum are given.

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