The characterizations of the stable perturbation of a closed operator by a linear operator in Banach spaces

Abstract

In this paper, we investigate the invertibility of $I_Y+\delta T{T}^{+}$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^{+}$ and $\delta T$ is a linear operator whose domain contains $D(T)$ and range is contained in $D(T^{+})$. The characterizations of the stable perturbation $T+\delta T$ of $T$ by $\delta T$ in Banach spaces are obtained. The results extend the recent main results of Huang's in Linear Algebra and its Applications.

arXiv comment9 pages, accepted by Linear Algebra and its Applications