Operator equations $AX+YB=C$ and $AX{A}^{\ast }+BY{B}^{\ast }=C$ in Hilbert $C^{\ast }$-modules

Z. Mousavi, R. Eskandari, M. S. Moslehian +1

Let $A,B$ and $C$ be adjointable operators on a Hilbert $C^{\ast }$-module $\mathcal{E}$. Giving a suitable version of the celebrated Douglas theorem in the context of Hilbert $C^{\ast }$-modu…