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

Abstract: 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 $\bar{T}^\dag$ and the upper bounds of $|\bar{T}^\dag|$ and $|\bar{T}^\dag -T^\dag|$. These results obtained in this paper extend and improve many related results in this area.