G-positive and G-repositive solutions to some adjointable operator equations over Hilbert C^{∗}-modules
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Abstract:
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 literature.
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Journal title
volume 39 issue 5
pages 971- 992
publication date 2013-10-15
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