Weighted Moore--Penrose inverses of adjointable operators on indefinite inner-product spaces
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Necessary and sufficient conditions are provided under which the weighted Moore--Penrose inverse $A^\dag_{MN}$ exists, 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.
Abstract
Necessary and sufficient conditions are provided under which the weighted Moore--Penrose inverse $A^\dag_{MN}$ exists, 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.
참고문헌 (15)
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