勷勤数学•专家报告

题      目：Quasi-projection pairs on Hilbert C*-modules

报  告  人：田晓怡  讲师  (邀请人：邓春源)

                                 广东警官学院

时      间：11月11日  19：00-20：00

地     点：数科院阶梯二楼报告厅

报告人简介:

       田晓怡，广东警官学院，讲师，研究方向：算子理论，泛函分析及其应用；硕博分别毕业于华南师范大学和上海师范大学，博士期间主持学生项目3项，获得省部级奖励1次，国家级奖励2次，目前在J. Operator Theory，Banach J. Math. Anal.，Linear Algebra Appl.，Linear Multilinear Algebra，Filomat 等知名期刊发表论文8篇。

摘      要：

       The aim of this paper is to give significant characterizations of some fundamental issues about idempotents on Hilbert C*-modules. Motivated by a couple of examples, a new term of quasi-projection pair (P,Q) on a Hilbert C*-module H is introduced, in which P is a projection, while Q is an idempotent satisfying PQ*P=PQP,  PQ*(I-P)=-PQ(I-P),  (I-P)Q*(I-P)=(I-P)Q(I-P), where I denotes the identity operator on H. Some basic properties of quasi-projection pairs are provided. For every idempotent Q on a Hilbert C*module H, it is shown that there always exist a projection denoted by m(Q), and an invertible operator W on H such that (m(Q),Q) is a quasi-projection pair satisfying  Q=W^{-1} PW and ‖I-W‖<1. Thus, a new formula for Q is derived based on m(Q), which is called the matched projection of Q. The matched projection m(Q) introduced in this paper for a general idempotent Q is a brand new object, which has many interesting features. Some fundamental results on m(Q) are derived.

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