G-投影算子的线性组合  

Linear Combinations of G-Projection Operators

作　　者：赵冰 海国君[1] 阿拉坦仓 ZHAO Bing;HAI Guojun;Alatancang(School of Mathematical Sciences,Inner Mongolia University,Hohhot O10021,China;College of Mathematics Science,Inner Mongolia Normal University,Hohhot O10022,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古大学学报（自然科学版）》2023年第5期462-468,共7页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金项目(11761052);内蒙古自然科学基金项目(2020ZD01)。

摘　　要：根据值域的关系,分别研究了G-投影算子的线性组合是G-投影算子的充要条件,以及G-投影算子与G-压缩算子及G-正算子的关系,并将Hilbert空间中投影算子的某些结论推广到G-投影算子上。最后,举例说明了结论的有效性。The necessary and sufficient conditions for the linear combinations of G-projectors to be a G-projector are given by the relation of their ranges.Moreover,the relations between G-projector,G-contractive operator and G-positive operator are characterized.Then,the corresponding results of the projector in Hilbert space are generalized to the G-projector.Finally,examples are given to illustrate the effectiveness of the conclusions.

关 键 词：G-投影算子 G-压缩算子 线性组合 值域 

分 类 号：O177.1[理学—数学]