The Reflexive Selfadjoint Solutions to Some Operator Equations

Abstract

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.