Ela Positive and Re-positive Solutions to Some Systems of Adjointable Operator Equations over Hilbert C−modules∗
نویسندگان
چکیده
A necessary and sufficient condition for the existence of the general common positive solution to equations A1X = C1, XB2 = C2, A3XA ∗ 3 = C3, A4XA ∗ 4 = C4 for operators between Hilbert C-modules is established, and an expression for the common positive solution to the equations is derived when the solvability conditions are satisfied. As an application, a new necessary and sufficient condition for the system of adjointable operator equations AX = C, XB = D over Hilbert C-modules to have a common Re-positive solution is proved. Moreover, an expression of the general Re-positive solution is derived when the consistent conditions are met. The results of this paper extend some known results in the literature.
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G-positive and G-repositive solutions to some adjointable operator equations over Hilbert C^{∗}-modules
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