报告题目：On Black Operator Matrices

报 告 人：邓春源（华南师范大学）

报告时间：2023年7月14日（周五）下午19:00-20:30

报告地点：逸夫楼C507

报告摘要：In this talk, the common characterizations and various individual properties of different generalized inverses are established. The explicit matrix expressions for various generalized inverses are obtained by using block operator matrix methods. Some subtle relationships between the properties of sub-blocks in operator matrices and their range relations are built. We analyze the matrix structures of various generalized inverses, suggest their applicable scopes and build their relationships with particular projections. We study the invertibility and the Moore-Penrose invertibility of 2×2 block matrix with Schur complement having closed range by using operator block matrices. The explicit expressions for the (P; Q)-outer generalized inverse based on the idempotent operators P and Q are given. We present a new interpretation of this relation which allows to generalize many known results for matrices to general Hilbert spaces. Several equivalent conditions for the core-EP, weak group inverse, m-weak group inverse and weak core inverse are presented. The brand new explicit expressions for the operator binary relations defined by various generalized inverses are obtained.

个人简介：邓春源，华南师范大学教授、博士生导师。2006年毕业于陕西师范大学数学科学学院并获得理学博士学位。2006年7月至今在华南师范大学任教，2012年9月到2013年9月在美国威廉玛丽学院进行学术访问。主持或参加多项国家和省级自然科学基金，参与完成的《算子矩阵及其应用研究》于2009年获得陕西省科技进步奖一等奖。多年来, 主要从事基础数学的教学和研究工作，自2000年以来, 先后在《数学学报》、《Proc. Amer.Math. Soc.》、《Linear Algebra Appl.》、《Studia Math.》、《J. Math. Anal. Appl.》、《Appl. Math.Comp.》、《Appl. Math. Letters》等国内外重要的数学学术期刊上发表论文80多篇。内容涉及算子谱论、算子矩阵理论、幂等算子理论、量子效应的分解与下确界问题等方面、Banach 格上正算子理论、矩阵扰动分析和算子广义逆理论等多个分支。近年来，研究兴趣主要集中在算子广义逆扰动分析和应用，算子分块技巧和算子谱理论在Grassmannia研究中的应用。