G. Song

[ 1 ] - G-positive and G-repositive solutions to some adjointable operator equations over Hilbert C^{∗}-modules

Some necessary and sufficient conditions are given for the existence of a G-positive (G-repositive) solution to adjointable operator equations $AX=C,AXA^{left( astright) }=C$ and $AXB=C$ over Hilbert $C^{ast}$-modules, respectively. Moreover, the expressions of these general G-positive (G-repositive) solutions are also derived. Some of the findings of this paper extend some known results in the...