Perturbation analysis of $A_{T,S}^{(2)}$ on Hilbert spaces
arXiv:1209.1767h-index: 13
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This is an incremental theoretical contribution for mathematicians working on operator theory and generalized inverses.
The paper studies how small perturbations in operators T, S, and A affect the generalized inverse A_{T,S}^{(2)} on Hilbert spaces, providing conditions for stability and explicit perturbation bounds.
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.