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Quadratic operator inequalities and linear-fractional relations

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Abstract

We study properties of solution sets of inequalities of the form

$$X^* AX + B^* X + X^* B + C \leqslant 0,$$

, where A, B, and C are bounded Hilbert space operators and A and C are self-adjoint. The following properties are considered: closedness and inferior points in Standard operator topologies, convexity, and nonemptiness.

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Authors and Affiliations

  1. Department of Math. And Comp., Sci. St.-John’s University, USA

    V. A. Khatskevich

  2. Department of Math., ORT Braude College, Israel

    M. I. Ostrovskii

  3. Department of Mathematics, Vologda Polytechnical Institute, Russia

    V. S. Shulman

Authors
  1. V. A. Khatskevich
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  2. M. I. Ostrovskii
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  3. V. S. Shulman
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Corresponding author

Correspondence to V. A. Khatskevich.

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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 41, No. 4, pp. 83–87, 2007

Original Russian Text Copyright © by V. A. Khatskevich, M. I. Ostrovskii, and V. S. Shulman

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Khatskevich, V.A., Ostrovskii, M.I. & Shulman, V.S. Quadratic operator inequalities and linear-fractional relations. Funct Anal Its Appl 41, 314–317 (2007). https://doi.org/10.1007/s10688-007-0031-x

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  • DOI: https://doi.org/10.1007/s10688-007-0031-x

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