C~*代数上方程ax=xax与ax=xa=xax的解  

Solutions to the Equations ax=xax and ax=xa=xax in C~* Algebra

作　　者：田学刚 王少英 TIAN Xuegang;WANG Shaoying(Department of Mathematics,Binzhou University,Binzhou 256603,Chin)

机构地区：[1]滨州学院理学院,山东滨州256603

出　　处：《太原师范学院学报（自然科学版）》2018年第2期18-21,24,共5页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山东省自然科学基金(ZR2016FQl6);滨州学院科研基金(BZXYLl505);滨州学院科研基金(BZXYLl604)

摘　　要：在C*代数中,利用元素的矩阵表示技巧和Moore-Penrose逆,研究方程ax=xax正则解的存在性,给出了该方程有正则解的充要条件,并给出了正则解的一般形式.此外,在两种情况下,得到方程ax=xa=xax有正则解的充要条件,并分别给出解的一般形式.In C＊algebra,using the block element matrix technique and the Moore-Penrose inverse,the existence of regular solutions for ax=xasis studied,the sucient and necessary conditions for that are obtained,and the general regular solutions are also given.Moreover,in two conditions,the sucient and necessary conditions for the existence of regular solutions of the equation ax=xa=xaxand the representation of the solutions are established.

关 键 词：正则解 方程 MOORE-PENROSE逆 不变投影 

分 类 号：O117.1[理学—数学]