THE SOLUTION TO THE SYSTEM OFPEDERSEN-TAKESAKI OPERATOR EQUATIONS

Let $mathscr{E}$ be a Hilbert $C^*$-module and $mathcal{L}(mathscr E)$ be the $C^*$-algebra of adjointable operators on $mathscr{E}$. We give a necessary conditions that for which the system of Pedersen--Takesaki equations in the setting of Hilbert $C^*$-modules has a positive solution.