算子方程AX＋X~＊B=C的解  

Solutions of the operator equation AX ＋ X＊B =C

作　　者：赵琳琳[1] 

机构地区：[1]德州学院数学系,山东德州253023

出　　处：《纯粹数学与应用数学》2012年第4期469-474,共6页Pure and Applied Mathematics

基　　金：国家自然科学基金(10971070;11071079)

摘　　要：利用算子的广义逆及相关投影,研究了一类算子方程的可解性,得到了方程可解的若干条件,并给出了解的一般表示.最后利用算子的矩阵表示,得到了此类算子方程可解的又一充要条件,进而丰富了这方面的研究.A class of the operator equations is studied by using the general inverse of the operator and its related projectors, some solvability conditions and a general solution to this equation are obtained. Finally, using the matrix form of the operator, another necessary and sufficient condition for the solvability of such operator equation is derived. These results enrich the research in this area.

关 键 词：HILBERT空间 算子方程 MOORE-PENROSE逆 

分 类 号：O177[理学—数学]