報告人: 許慶祥教授、鄧春源教授
講座日期：2020-11-02
講座時間：14:40
報告地點：騰訊會議（935 822 979）
主辦單位：數(shù)學與信息科學學院
報告題目一：Generalized parallel sum of adjointable operators on Hilbert C*-modules
報告人: 許慶祥教授
講座時間：14:40
報告人簡介：
許慶祥, 上海師范大學數(shù)理學院教授、博士生導師。1985年1989年本科就讀于浙江師范大學數(shù)學系，1989年至1995年研究生就讀于復旦大學數(shù)學研究所，師從嚴紹宗教授和陳曉漫教授。1995年到上海師范大學數(shù)學系工作至今。
近年來主要從事算子理論和矩陣方面的研究工作，被MathSinNet收錄文章69篇, 部分文章發(fā)表于SIAM J. Numer. Anal., SIAM J. Matrix Anal. Appl., J. London Math. Soc., J. Operator Theory和Linear Algebra Appl.等期刊上. 目前擔任期刊Advances in Operator Theory和Facta Universitatis, Series: Mathematics and Informatics的編委。
報告簡介：
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.
報告題目二：On the parallel addition and subtraction of operators on a Hilbert space
報告人: 鄧春源教授
講座時間：16:00
報告人簡介：
鄧春源，華南師范大學教授、博士生導師。2000至2006年就讀于陜西師范大學數(shù)學與信息科學學院，師從杜鴻科教授，先后獲理學碩士學位和理學博士學位。2006年7月至今在華南師范大學工作，先后任講師(2006)、副教授(2007)、教授(2011)，博導（2014）。在此期間，從2012年9月到2013年9月在美國威廉瑪麗學院進行學術訪問。主要從事算子理論與算子代數(shù)方面的研究工作，在算子矩陣理論、冪等算子理論、算子的廣義逆理論等方面取得了一系列研究成果。主持或參加多項省部級自然科學基金，已在國內(nèi)外刊物上發(fā)表論文70余篇。
報告簡介：
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.
