Hilbert空间上投影算子的BirkhoffJames正交性  

Birkhoff-James Orthogonality of the Projections on a Hilbert Space

作　　者：李珊珊 孟庆[1] LI Shanshan;MENG Qing(School of Mathematical Sciences, Qufu Normal University, Qufu 271365, China)

机构地区：[1]曲阜师范大学数学科学学院,山东曲阜273165

出　　处：《湖州师范学院学报》2020年第4期14-18,共5页Journal of Huzhou University

基　　金：中国博士后科学基金项目(2018M642633).

摘　　要：讨论Hilbert空间上投影算子的Birkhoff-James正交性.利用Birkhoff-James正交性的定义和性质,结合投影算子技巧,给出有限维Hilbert空间上投影算子的Birkhoff-James正交的充要条件,并讨论Birkhoff-James正交与强Birkhoff-James正交的等价性和正交性的关系.In this paper,we discuss Birkhoff-James orthogonality of the projections.By using the definition and properties of the Birkhoff-James orthogonality and some technique about projections,some equivalent conditions about Birkhoff-James orthogonality of the projections on a Hilbert space of finite dimensional are given.We also discuss the relationship between Birkhoff-James orthogonality and strong Birkhoff-James orthogonality.

关 键 词：HILBERT空间 投影算子 Birkhoff-James正交 

分 类 号：O177.1[理学—数学]