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In this paper, the positive operator solutions to operator equation  X − A ∗ X − t A = Q (t &gt; 1) are studied in infinite dimensional Hilbert space. Firstly, the range of norm and the spectral radius of the solution to the equation are given. Secondly, by constructing effective iterative sequence, it gives some conditions for the existence of positive operator solutions to operator equation  X − A ∗ X − t A = Q (t &gt; 1). The relations of these operators in the operator equation are given.

journal of mathematics

On the Positive Operator Solutions to an Operator Equation <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>X</mi> <mo>−</mo> <msup> <mrow> <mi>A</mi> </mrow> <mi>∗</mi> </msup> <msup> <mrow> <mi>X</mi> </mrow> <mrow> <mo>−</mo> <mi>t</mi> </mrow> </msup> <mi>A</mi> <mo>=</mo> <mi>Q</mi> </math>

On the Positive Operator Solutions to an Operator Equation X − A ∗ X − t A = Q

On the Positive Operator Solutions to an Operator Equation $X - A^{*} X^{- t} A = Q$