The Reflexive Selfadjoint Solutions to Some Operator Equations (Communications in Mathematical Research, 2021)
In this paper, we study the existence of the reflexive, reflexive self-adjoint and reflexive positive solutions to some operator equations with respectto the generalized reflection operator dual $(P,Q)$. We derive necessary and sufficient conditions for the solvability of these equations and provide a detaileddescription of the solutions in the solvable case by using the Moore-Penroseinverses.
Keywords: $(P; Q)$ reflexive solution; operator equation; positive operator.