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 Weighted Moore--Penrose inverses of adjointable operators on indefinite inner-product spaces J. Korean Math. Soc.Published online September 24, 2019 Mengjie Qin, Qingxiang Xu, and Ali Zamani Shanghai Normal University, Farhangian University Abstract : Necessary and sufficient conditions are provided under which the weighted Moore--Penrose inverse $A^\dag_{MN}$ is existent, where $A$ is an adjointable operator between Hilbert $C^*$-modules, and the weights $M$ and $N$ are only self-adjoint and invertible. Relationship between weighted Moore--Penrose inverses $A^\dag_{MN}$ is clarified when $A$ is fixed, whereas $M$ and $N$ are variable. Perturbation analysis for the weighted Moore--Penrose inverse is also provided. Keywords : Hilbert $C^*$-module, weighted Moore--Penrose inverse, indefinite inner-product space MSC numbers : 46L08, 15A09, 47A05 Full-Text :