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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FAA_2007_41_4_a8,
     author = {M. I. Ostrovskii and V. A. Khatskevich and V. S. Shulman},
     title = {Operator {Quadratic} {Inequalities} and {Linear} {Fractional} {Relations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {83--87},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a8/}
}
TY  - JOUR
AU  - M. I. Ostrovskii
AU  - V. A. Khatskevich
AU  - V. S. Shulman
TI  - Operator Quadratic Inequalities and Linear Fractional Relations
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2007
SP  - 83
EP  - 87
VL  - 41
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a8/
LA  - ru
ID  - FAA_2007_41_4_a8
ER  - 
%0 Journal Article
%A M. I. Ostrovskii
%A V. A. Khatskevich
%A V. S. Shulman
%T Operator Quadratic Inequalities and Linear Fractional Relations
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2007
%P 83-87
%V 41
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2007_41_4_a8/
%G ru
%F FAA_2007_41_4_a8
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/