- Journal Home
- Volume 41 - 2025
- Volume 40 - 2024
- Volume 39 - 2023
- Volume 38 - 2022
- Volume 37 - 2021
- Volume 36 - 2020
- Volume 35 - 2019
- Volume 34 - 2018
- Volume 33 - 2017
- Volume 32 - 2016
- Volume 31 - 2015
- Volume 30 - 2014
- Volume 29 - 2013
- Volume 28 - 2012
- Volume 27 - 2011
- Volume 26 - 2010
- Volume 25 - 2009
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0013}, url = {http://global-sci.org/intro/article_detail/cmr/19440.html} }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.