Quadratic operator inequalities and linear-fractional relations
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We study properties of solution sets of inequalities of the form
, where A, B, and C are bounded Hilbert space operators and A and C are self-adjoint. The following properties are considered: closedness and inferior points in Standard operator topologies, convexity, and nonemptiness.
$$X^* AX + B^* X + X^* B + C \leqslant 0,$$
Key wordsHilbert space bounded linear operator weak operator topology operator inequality
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