The characterizations of the stable perturbation of a closed operator by a linear operator in Banach spaces
arXiv:1209.17665 citationsh-index: 13
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For mathematicians working in operator theory, this is an incremental extension of known perturbation results to more general settings.
The paper characterizes when the perturbation T+δT of a closed operator T by a linear operator δT remains invertible in Banach spaces, extending previous results by Huang.
In this paper, we investigate the invertibility of $I_Y+δTT^+$ when $T$ is a closed operator from $X$ to $Y$ with a generalized inverse $T^+$ and $δT$ is a linear operator whose domain contains $D(T)$ and range is contained in $D(T^+)$. The characterizations of the stable perturbation $T+δT$ of $T$ by $δT$ in Banach spaces are obtained. The results extend the recent main results of Huang's in Linear Algebra and its Applications.