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

arXiv comment9 pages