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arXiv · 1212.1851

The characterizations and representations for the generalized inverses with prescribed idempotents in Banach algebras

Jianbing Cao·Yifeng Xue
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Abstract

In this paper, we investigate the various different generalized inverses in a Banach algebra with respect to prescribed two idempotents $p$ and $q$. Some new characterizations and explicit representations for these generalized inverses, such as $a^{(2)}_{p,q}$, $a^{(1,2)}_{p,q}$ and $a^{(2,l)}_{p,q}$ will be presented. The obtained results extend and generalize some well--known results for matrices or operators.

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BibTeXRIS

Jianbing Cao, Yifeng Xue. 2012-12-09. The characterizations and representations for the generalized inverses with prescribed idempotents in Banach algebras. https://arxiv.org/abs/1212.1851

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