Splitting of Operators and Operator Equations  

作　　者：Chun Yuan DENG Wan Yu ZHANG 

机构地区：[1]School of Mathematics Science,South China Normal University,Guangzhou 510631,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第6期1085-1100,共16页数学学报（英文版）

摘　　要：In this paper,we consider the splitting operators into the product of two positive operators.For given operators A and T∈B(H)with A≥0 and R(A)=R(T),if T can be splitted as T=AX for some positive operator X,then the existence of X and the properties of T are studied.The related research are the solutions of operator equations T=XAX and TX=XAX,which have some particular properties and broad applications in many fields.The conditions for the existence of solutions or idempotent solutions of these kinds of equations are studied and new representations of the general solutions are given.

关 键 词：PROJECTION positive operator operator equation Moore-Penrose inverse 

分 类 号：O177[理学—数学]