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2020•Linear and Multilinear AlgebraRequires access

The g-Drazin inverse of the sum in Banach algebras

Huanyin Chen, Marjan Sheibani

Open publisher page 6 citations

Abstract

Let A be a complex Banach algebra. An element a∈A has g-Drazin inverse if there exists b∈A such that b=bab,ab=ba,a−a2b∈Aqnil. New additive results for the g-Drazin inverse in a Banach algebra are presented. These extend the main results of Deng and Wei (J. Math. Analysis Appl., 379(2010), 313–321) and Wang et al. (Filomat, 30(2016), 1185–1193).

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What this paper is about

Let A be a complex Banach algebra. An element a∈A has g-Drazin inverse if there exists b∈A such that b=bab,ab=ba,a−a2b∈Aqnil. New additive results for the g-Drazin inverse in a Banach algebra are presented. These extend the main results of Deng and Wei (J. Math. Analysis Appl., 379(2010), 313–321) and Wang et al. (Filomat, 30(2016), 1185–1193).

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Available abstract

Let A be a complex Banach algebra. An element a∈A has g-Drazin inverse if there exists b∈A such that b=bab,ab=ba,a−a2b∈Aqnil. New additive results for the g-Drazin inverse in a Banach algebra are presented. These extend the main results of Deng and Wei (J. Math. Analysis Appl., 379(2010), 313–321) and Wang et al. (Filomat, 30(2016), 1185–1193).

Key concepts: Drazin inverse, Banach algebra, Mathematics, Inverse, Element (criminal law), Pure mathematics, Banach space, Algebra over a field

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