报告题目 (Title)：Completion of operator matrices with application to solving operator equations (算子矩阵的补全及其在求解算子方程中的应用)
报告人 (Speaker)： Dragana Cvetkovi Ili 教授（Kuwait University）
报告时间 (Time)：2024年 12 月6日 (周五) 10:30-12:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：王卿文
报告摘要： We will present certain necessary and sufficient conditions for the existence of a non-zero solution of the operator equation XAX = BX. Furthermore, we derive two possible representations of an arbitrary solution as a 2 × 2 operator matrix which allows us to discuss the existence of an invertible and a positive solution but also to open the discussion to the existence of any type of solutions using related results for completions of 2×2 operator matrices. Also, we consider the operator equation XAX = AX which is closely related to the “invariant subspace problem” and describe the set of all right(left) invertible and all Fredholm solutions.