Solutions of Sylvester equation in -modular operators
| Autor: | M. Khanehgir, M. Mohammadzadeh Karizaki, Z. N. Moghani |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
business.industry 010102 general mathematics 010103 numerical & computational mathematics Modular design 01 natural sciences symbols.namesake Operator (computer programming) symbols Lyapunov equation 0101 mathematics Special case Sylvester equation Hilbert C*-module business Moore–Penrose pseudoinverse Mathematics |
| Zdroj: | Ukrains’kyi Matematychnyi Zhurnal. 73:354-369 |
| ISSN: | 1027-3190 |
| DOI: | 10.37863/umzh.v73i3.152 |
| Popis: | UDC 517.9 We study the solvability of the Sylvester equation $AX + Y B = C$ and the operator equation $AXD + FY B = C$ in the general setting of the adjointable operators between Hilbert $C^*$ -modules. Based on the Moore – Penrose inverses of the associated operators, we propose necessary and sufficient conditions for the existence of solutions to these equations, and obtain the general expressions of the solutions in the solvable cases. We also provide an approach to the study of the positive solutions for a special case of Lyapunov equation. |
| Databáze: | OpenAIRE |
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