This article is cited in 2 papers

Brief communications

Operator Quadratic Inequalities and Linear Fractional Relations

M. I. Ostrovskii^a, V. A. Khatskevich^b, V. S. Shulman<sup>c

a</sup> St. John's University
^b International College of Technology
^c Vologda State Technical University

Abstract: 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.

UDC: 917.983.248

Received: 20.10.2005

DOI: 10.4213/faa2884

 English version: Functional Analysis and Its Applications, 2007, 41:4, 314–317

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