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Funktsional'nyi Analiz i ego Prilozheniya, 2007, Volume 41, Issue 4, Pages 83–87
DOI: https://doi.org/10.4213/faa2884 (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
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DOI: https://doi.org/10.4213/faa2884
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.
Received: 20.10.2005
English version:
Functional Analysis and Its Applications, 2007, Volume 41, Issue 4, Pages 314–317
DOI: https://doi.org/10.1007/s10688-007-0031-x
Bibliographic databases:
Document Type: Article
UDC: 917.983.248
Language: Russian
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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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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