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Perturbation analysis for the generalized inverses with prescribed idempotents in Banach algebras (1301.4314v1)
Published 18 Jan 2013 in math.FA, math.NA, and math.OA
Abstract: In this paper, we first study the perturbations and expressions for the generalized inverses $a{(2)}_{p,q}$, $a{(1, 2)}{p,q}$, $a{(2, l)}{p,q}$ and $a{(l)}_{p,q}$ with prescribed idempotents $p$ and $q$. Then, we investigate the general perturbation analysis and error estimate for some of these generalized inverses when $p,\,q$ and $a$ also have some small perturbations.