Geodesic
Operator Quadratic Inequalities and Linear Fractional Relations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 83-87.

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Properties of sets of solutions of inequalities of the form $$ X^{\ast}AX + B^{\ast}X + X^{\ast}B + C \le 0 $$ are studied, where $A$, $B$, $C$ are bounded Hilbert space operators, $A$ and $C$ are self-adjoint. Properties under consideration: closeness and interior points in standard operator topologies, convexity, non-emptiness.
Keywords: Hilbert space, bounded linear operator, weak operator topology, operator inequalities. 
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M. I. Ostrovskii; V. A. Khatskevich; V. S. Shulman. Operator Quadratic Inequalities and Linear Fractional Relations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 41 (2007) no. 4, pp. 83-87. http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a8/

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