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On the operator equation \(AX-XB+XDX=C\)

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Abstract

By application of the generalized Drazin inverse a method for solving Riccati and Lyapunov operator equations in Hilbert space are given. Results are applied to the problem of finding general solutions for Cauchy problems for Riccati and Lyapunov operator differential equations.

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  1. Laboratory of Mathematical Techniques (LTM), Department of Mathematics, Faculty of Mathematics and Informatics, University of Batna 2, 05078, Batna, Algeria

    A. Bezai & F. Lombarkia

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  1. A. Bezai
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  2. F. Lombarkia
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Bezai, A., Lombarkia, F. On the operator equation \(AX-XB+XDX=C\). Rend. Circ. Mat. Palermo, II. Ser 72, 4179–4187 (2023). https://doi.org/10.1007/s12215-023-00887-3

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