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Solutions of the Sylvester Equation in C*-Modular Operators

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Ukrainian Mathematical Journal Aims and scope

We study the solvability of the Sylvester equation AX + YB = C and the operator equation AXD + FYB = C in the general setting of adjointable operators between Hilbert C*-modules. On the basis of the Moore–Penrose inverses of the associated operators, we establish necessary and sufficient conditions for the existence of solutions to these equations and obtain general expressions for the solutions in the solvable cases. We also propose an approach to the investigation of positive solutions for a special case of Lyapunov equation.

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Authors and Affiliations

  1. Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    Z. Niazi Moghani

  2. Department of Computer Engineering, University of Torbat Heydarieh, Torbat Heydarieh, Iran

    M. Mohammadzadeh Karizaki

  3. Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

    M. Khanehgir

Authors
  1. Z. Niazi Moghani
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  2. M. Mohammadzadeh Karizaki
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  3. M. Khanehgir
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Corresponding author

Correspondence to M. Khanehgir.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 3, pp. 354–369, March, 2021. Ukrainian DOI: 10.37863/umzh.v73i3.152.

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Moghani, Z.N., Karizaki, M.M. & Khanehgir, M. Solutions of the Sylvester Equation in C*-Modular Operators. Ukr Math J 73, 414–432 (2021). https://doi.org/10.1007/s11253-021-01933-y

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  • DOI: https://doi.org/10.1007/s11253-021-01933-y

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