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In this paper, we study the existence of the reflexive, reflexive self-adjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual $(P,Q)$. We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.
}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0006}, url = {http://global-sci.org/intro/article_detail/cmr/18739.html} }In this paper, we study the existence of the reflexive, reflexive self-adjoint and reflexive positive solutions to some operator equations with respect to the generalized reflection operator dual $(P,Q)$. We derive necessary and sufficient conditions for the solvability of these equations and provide a detailed description of the solutions in the solvable case by using the Moore-Penrose inverses.