Solutions of Sylvester equation in -modular operators-Reference-Cited by-同舟云学术

Solutions of Sylvester equation in -modular operators

Published:2021-03-11 Issue:3 Volume:73 Page:354-369
ISSN:1027-3190
Container-title:Ukrains’kyi Matematychnyi Zhurnal
language:
Short-container-title:Ukr. Mat. Zhurn.

Author:

Khanehgir M.,Moghani Z. N.,Mohammadzadeh Karizaki M.

Abstract

UDC 517.9 We study the solvability of the Sylvester equation and the operator equation in the general setting of the adjointable operators between Hilbert -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.

Publisher

Institute of Mathematics National Academy of Sciences of Ukraine

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