NASep 9, 2012
The characterizations of the stable perturbation of a closed operator by a linear operator in Banach spacesFapeng Du, Yifeng Xue
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.
RAOct 5, 2012
The perturbation of the group inverse under the stable perturbation in a unital ringFapeng Du, Yifeng Xue
Let $\R $ be a ring with unit 1 and $a\in \R, \bar{a}=a+δa\in \R $ such that $a^#$ exists. In this paper, we mainly investigate the perturbation of the group inverse $a^#$ on $\R$. Under the stable perturbation, we obtain the explicit expressions of $\bar{a}^#$. The results extend the main results in Xue (2007), and Xue and Chen (2007) and some related results in Xue (2012). As an application, we give the representation of the group inverse of the matrix d&b c&0 on the ring $\R$ for certain $d, b, c\in\R$.
NAJul 7, 2012
Perturbation analysis of $A_{T,S}^{(2)}$ on Banach spacesFapeng Du, Yifeng Xue
In this paper, the perturbation problems of $A_{T,S}^{(2)}$ are considered. By virtue of the gap between subspaces, we derive the conditions that make the perturbation of $A_{T,S}^{(2)}$ is stable when $T,S$ and $A$ have suitable perturbations. At the same time, the explicit formulas for perturbation of $A_{T,S}^{(2)}$ and new results on perturbation bounds are obtained.
FAJan 31, 2013
Perturbation analysis for Moore-Penrose inverse of closed operators on Hilbert spacesFapeng Du, Yifeng Xue
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.
NASep 19, 2012
Perturbation analysis of $A_{T,S}^{(2)}$ on Hilbert spacesFapeng Du, Yifeng Xue
In this paper, we investigate the perturbation analysis of $A_{T,S}^{(2)}$ when $T,\,S$ and $A$ have some small perturbations on Hilbert spaces. We present the conditions that make the perturbation of $A_{T,S}^{(2)}$ is stable. The explicit representation for the perturbation of $A_{T,S}^{(2)}$ and the perturbation bounds are also obtained.