Year: 2021
Author: Jianlong Chen, Zhengqian Zhu, Guiqi Shi
Communications in Mathematical Research, Vol. 37 (2021), Iss. 4 : pp. 484–495
Abstract
Let $\mathscr{A}$ be a complex Banach algebra and $J$ be the Jacobson radical of $\mathscr{A}$. (1) We firstly show that $a$ is generalized Drazin invertible in $\mathscr{A}$ if and only if $a+J$ is generalized Drazin invertible in $\mathscr{A}$/$J$. Then we prove that $a$ is pseudo Drazin invertible in $\mathscr{A}$ if and only if $a+J$ is Drazin invertible in $\mathscr{A}$/$J$. As its application, the pseudo Drazin invertibility of elements in a Banach algebra is explored. (2) The pseudo Drazin order is introduced in $\mathscr{A}$. We give the necessary and sufficient conditions under which elements in $\mathscr{A}$ have pseudo Drazin order, then we prove that the pseudo Drazin order is a pre-order.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0013
Communications in Mathematical Research, Vol. 37 (2021), Iss. 4 : pp. 484–495
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Drazin inverse pseudo Drazin inverse generalized Drazin inverse.
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