Solutions of Sylvester equation in $C^*$-modular operators

• Date: 2021
• Main Authors: Moghani, Z. Niazi, Mohammadzadeh Karizaki, M., Khanehgir, M.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/152
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 suffi...