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

Document Type : Research Paper

Author

University of Weifang, P. R. China

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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Main Subjects