Solutions for Types of Operator Equations

The aim of this work is to study the solvability of some specific types of non-linear operator equations and some properties of mapping of operator equations, also present as following: (1) The solvability of general solutions for bounded non-linear operator equations AXB=C, AX*B=C and A*XB*+BX*A=C via pseudo inverse of operators A and B have been Studied and Discussed. (2) The general self-adjoint solutions of operator equations AXB=C, AXA*=C and A*XB*+BX*A=C via pseudo inverse of operators A and B have been given. (3) The common solution to the operator equations AX=C and XB=D. Also to the operator equation AX=C with the system of operator equations XBi=Di where i=1....n has been Introduce. At last the common solution to the system of operator equations AXB=C, BXA=D, AXA=E and BXB=F has been given. (4) The common Hermitian solution to the operator equations AX=C and XB=D. Also the system of operator equations AXA*=C, A*XA=D, AXA=0 and A*XA*=0 have been given.