Solutions to some systems of adjointable operator
equations over Hilbert $C^*$modules
Z. Niazi Moghani, M. Khanehgir
In this paper, by using operator matrix techniques, we present necessary and sufficient conditions for the existence of a
solution to the system of equations $AXD+FX^{*}B=C,$ $GXF^{*}+FX^{*}G^{*}=H$ for adjointable operators between Hilbert
$C^*$modules, and derive an expression for the general solution to the system. We establish necessary and sufficient conditions
for the existence of a solution to the system of adjointable operator equations $AXF=H_{1},$ $CXD=H_{2},$ $BXD=H_{3}$ over Hilbert
$C^*$modules. Some of the findings of this paper extend some known results in the literature.
Tbilisi Mathematical Journal, Vol. 12(3) (2019), pp. 93107
