Perturbation analysis for Moore-Penrose inverse of closed operators on Hilbert spaces

In this paper, we investigate the perturbation for the Moore-Penrose inverse of closed operators on Hilbert spaces. By virtue of a new inner product defined on $H$, we give the expression of the Moore-Penrose inverse $\bar{T}^†$ and the upper bounds of $\|\bar{T}^†\|$ and $\|\bar{T}^†-T^†\|$. These results obtained in this paper extend and improve many related results in this area.

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