Solutions to the operator equation AXB=C
Shaoying Wang · Journal of Shandong University · 2010
Using the block operator matrix technique and the generalized inverse of operator,the solutions to the operator equation AXB=C are studied in infinite Hilbert space.The sufficient and necessary condition for the existence of solutions to the equation AXB=C and the representation of the solutions are established.When R(A)R(B) or R(B)R(A),the sufficient and necessary condition for the existence of positive solutions of the equation AXB=C and the general form of the positive solutions are also derived.