Solutions to the System of Operator Equations A1X=C1, XB2=C2, and A3XB3=C3 on Hilbert C*-Modules

الملخص EN

We study the solvability of the system of the adjointable operator equations A1X=C1, XB2=C2, and A3XB3=C3 over Hilbert C*-modules.

We give necessary and sufficient conditions for the existence of a solution and a positive solution of the system.

We also derive representations for a general solution and a positive solution to this system.

The above results generalize some recent results concerning the equations for operators with closed ranges.