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                On the parallel addition and subtraction of operators on a Hilbert space


                主讲人:邓春源  华南师范大学教授


                地点:腾讯会议 901 256 150


                主讲人介绍:邓春源,湖北丹江口市人,华南师范大学教授、博士生导师。2000至2006年就读于陕西师范大学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。2006  年7月至今在华南师范大学工作,在此期间,从2012年9月到2013年9  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。

                内容介绍:We extend the operations of parallel addition A : B and parallel subtraction A÷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  fifinite-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. Some conditions for the relations A? : B? = (A + B)? , B  = (A : B) ÷ A, (AC) ÷ (BC) = (A ÷ B)C, A ÷ B = (P(A?-B?)P)? , B = A : (B ÷ A),  (CA) : (CB) = C(A : B) to be true are studied and the solution of the equation A  : X = B is investigated. Moreover, some relationships between the parallel  addition and subtraction of projections are obtained.