Perturbation analysis for the generalized inverses with prescribed idempotents in Banach algebras
arXiv:1301.43144 citationsh-index: 15
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Provides theoretical tools for analyzing perturbations of generalized inverses, relevant to researchers in functional analysis and operator theory.
The paper derives perturbation bounds and error estimates for several types of generalized inverses with prescribed idempotents in Banach algebras, extending known results to more general settings.
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.