On the Operator Equations AX=XAX and AX=XA=XAX
Gui-Mei An, Zhaofang Bai, Shuanping Du · 2003
In this paper, we give the representation of the solution set of the operator equation AX=XAX in terms of the invariant subspaces of A and the representation of solution set of AX=XA=XAX in the cases that A is a normal operator or an operator with dense range or with injectivity. We also give a sufficient and necessary condition for a normal operator X to be a solution of equation XAX=XA=XA.