The solutions to the operator equation TXS^* -SX^*T^*=A in Hilbert C^*-modules

In this paper, we find explicit solution to the operator equation TXS^* -SX^*T^*=A in the general setting of the adjointable operators between Hilbert C^*-modules, when T,S have closed ranges and S is a self adjoint operator.

Keywords:

Operator equation , Moore-Penrose inverse , Hilbert C^*-module