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
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