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Funktsional. Anal. i Prilozhen., 2007, Volume 41, Issue 4, Pages 83–87 (Mi faa2884)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Operator Quadratic Inequalities and Linear Fractional Relations

M. I. Ostrovskiia, V. A. Khatskevichb, V. S. Shulmanc

a 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

DOI: https://doi.org/10.4213/faa2884

Full text: PDF file (150 kB)
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English version:
Functional Analysis and Its Applications, 2007, 41:4, 314–317

Bibliographic databases:

UDC: 917.983.248
Received: 20.10.2005

Citation: M. I. Ostrovskii, V. A. Khatskevich, V. S. Shulman, “Operator Quadratic Inequalities and Linear Fractional Relations”, Funktsional. Anal. i Prilozhen., 41:4 (2007), 83–87; Funct. Anal. Appl., 41:4 (2007), 314–317

Citation in format AMSBIB
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\paper Operator Quadratic Inequalities and Linear Fractional Relations
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\pages 83--87
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    This publication is cited in the following articles:
    1. Tian Y., “Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications”, Linear Algebra Appl., 437:3 (2012), 835–859  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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