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第三届广义逆及其应用研讨会

1.      许庆祥  上海师范大学

题目:Norm estimations for the Moore-Penrose inverse of the weak perturbation of Hilbert $C^*$-module operators

摘要: Let $mathfrak{A}$ be a $C^*$-algebra, $H$ and $K$ be Hilbert $mathfrak{A}$ modules and $mathcal{L}(H,K)$ be the set of all adjointable operators from $H$ to $K$. A multiplicative perturbation $M$ of a Moore-Penrose invertible operator $Tinmathcal{L}(H,K)$ has the form $M=ETF^*$ with $Einmathcal{L}(K,K)$ and $Finmathcal{L}(H,H)$, which can be expressed alternately as $M=ETT^dagcdot Tcdot (FT^dag T)^*=L_{E,T}cdot Tcdot R_{F,T}^*$, where $T^dag$ is the Moore-Penrose inverse of $T$ and $$L_{E,T}=ETT^dag+I_K-TT^dag,  R_{F,T}=F T^dag T+I_H-T^dag T. $$ In view of the above $ETT^dag$, $FT^dag T$, $L_{E,T}$ and $R_{F,T}$, the relationship between various types of multiplicative perturbations are investigated, and formulas for  $M^dag$, $MM^dag$ and $M^dag M$ are derived in the case that $M$ is a weak perturbation of $T$. Based on these derived formulas, some norm computations are carried out by using certain $C^*$-algebraic techniques, through which new norm estimations for $M^dag-T^dag$ are obtained. As applications, perturbation estimations for the solutions to the least squares problems are provided. The sharpness of the newly obtained estimations are illustrated by several numerical examples.

 

 

2. 杜乃林    武汉大学

题目:On ad-nonprojection method for stable approximation to infinite-dimensional Moore-Penrose inverse

摘要: This talk presents ad-nonprojection method for approximation to infinite-dimensional Moore-Penrose inverse, which includes generalized projection method as a special case. The main result gives characteristics of perfect convergence, weak perfect convergence, and uniform perfect convergence of ad-nonprojection method. The result is a generalization of several fundamental theorems known.

 

3. Jiu Ding,  University of Southern Mississippi

题目:Some notes on the perturbation of generalized inverses

摘要: We weaken the usual assumption of perturbation theorems for operator equations in the case of commuting perturbations, using the spectral radius. And we provide a duality relation between Nashed’s condition and the stable perturbation condition on generalized inverses of bounded linear operators.

 

4. 邓春源   华南师范大学

题目:New results for mixed-type generalized inverses of the products of two operators

摘要: Let $A$, $B$ and $AB$ be closed range operators. The explicit matrix expressions for $K$-generalized inverses $AK$, $BK$ and $(AB)K$  when $Kin {{1}$, ${1, 2}$, ${1, 3}$, ${1, 4}$,  ${1, 2, 3}$, ${1, 2, 4}$, ${1, 3, 4}$, ${1, 2, 3, 4}}$ are obtained by using block operator matrix methods. Some subtle relationships between the properties of sub-blocks in operator matrices $A$, $B$ and their range relations are built. New necessary and sufficient conditions for the equivalent relations, inclusion relations and mixed-type generalized inverses relations among $AK$, $BK$ and $(AB)K$ are presented. Some recent mixed-type reverse-order laws results are covered and many new mixed-type generalized inverses relations are established by using this block-operator matrix technique.

 

5. 盛兴平  阜阳师范学院

题目:Computing the outer inverse through elementary operations based on an explicit representation

摘要: In this paper, we first derive a novel explicit representation which is simpler than that by Ji (2005) of the outer inverse $A^{(2)}_{T,S}$ for a matrix $Ain C^{m imes n}$ with the prescribed range $T$ and null space $S$. Next a new algorithm for computing the outer inverse $A^{(2)}_{T,S}$ which is based on the improving representation through elementary operations on an appropriate partitioned matrix is proposed and investigated. The computational complexity of the introduced algorithm is also analyzed in detailed. In the end, an example is presented to illustrate the new method. 

 

6. 王宏兴  广西民族大学

题目:关于非减序类偏序问题的研究

摘要: 介绍多个非减序类偏序及其性质结构。建立一类非减序类偏序:CL偏序,并简述其性质特征等。

 

7. 王 龙  扬州大学

题目:Some results on one-sided (b,c) inverses

摘要: In this talk, some results on one-sided (b,c) inverses are given. As applications, we introduce the notion of a (generalized) right core inverse and give its characterizations and expressions. Then, we provide the relation schema of (one-sided) core inverses, (one-sided) pseudo core inverses and EP elements. Finally, we present the characterizations of a class of special one-sided generalized inverses.

 

8. 朱辉辉  合肥工业大学

题目:On DMP inverses and m-EP elements in rings

摘要: Let R be a unital *-ring. In this paper, we introduce pseudo DMP inverses and generalized m-EP elements in R, which can been seen as extensions of DMP inverses and m-EP matrices, respectively. Also, we investigate both pseudo DMP inverses and generalized m-EP elements for their characterizations and properties.

 

9. 许三长  淮阴工学院

题目:Absorption laws for the core inverse

摘要: Let R be a unital ring with involution. Given two core invertible elements a,b in R, we investigate the absorption law for the core inverse in virtue of the equality of two projections. 

 

10. 赵汝菊  扬州大学

题目:Some characterizations of EP element and (b,c)-inverse

摘要: The aim of this paper is to describe the elements in rings with involution which are EP. Especially, we reduce the preliminary requirements met in some existing results. In addition, we investigate the sufficient and necessary condition for a ring to be a strongly left min-Abel ring by means of (b,c)-inverse of a. 

 

 

 

报告时间:20181013-14 上午8:30 开始

报告地点:蓝天大厦玉蜻蜓雅致酒店 三楼第二会议室
主办单位:数学科学学院


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