报告题目：

operators and generalized pencilsof pairs of projections

报 告 人：邓春源 教授 华南师范大学

邀请人：王帅杰

报告时间：2022年12月03日（周六）10：40-11：40

腾讯会议ID：925 728 734密码：221203

报告人简介：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，主要从事基础数学的教学和研究工作，主持或参加多项国家和省级自然科学基金，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、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研究中的应用等。

报告摘要：In this talk, the characterizations and properties of

operators and generalizedpencils of pairs of projections are established. Let

be a partial isometry. An operator

is said to be

if

and

. Some basic properties of

operators are given. The invariant characterizations that sum and product oftwo

operators still keep to be

are obtained.The properties of the generalized pencil

of pair (P,Q) of projections at

are investigated.Using Halmos decomposition theory for orthogonalprojections we give some equivalent conditions for which

is the generalized penciland study the spectrum properties of this generalized pencil

. We prove that thegeneralized pencil

is similar to a diagonal operator under some conditions. The spectrum relations among the generalized pencil

and projections

are established.Further, we give the necessary and sufficient conditions under which the generalizedpencil

is a Fredholm operator, a compact operator and a selfadjoint operator, respectively. Finally, the generalized pencils of pairs of idempotents are studied.

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