The solutions to some operator equations with corresponding operators not necessarily having closed ranges
Wenting Liang, Chunyuan Deng · Linear and Multilinear Algebra · 2018
In this paper, we study the solvability of the operator equations in the general setting of infinite-dimensional Hilbert space with corresponding operators no necessarily having closed range. We get the necessary and sufficient conditions for the existences of the solutions and obtain formulae in each case for the general selfadjoint, positive and real positive solutions to these operator systems.