We study the solvability of the system of the adjointable operator equations , , and over Hilbert -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.
"Solutions to the System of Operator Equations , , and on Hilbert -Modules." Abstr. Appl. Anal. 2013 (SI45) 1 - 8, 2013. https://doi.org/10.1155/2013/826564