Year: 2021
Author: Jianlong Chen, Zhengqian Zhu, Guiqi Shi
Communications in Mathematical Research , Vol. 37 (2021), Iss. 4 : pp. 484–495
Abstract
Let A be a complex Banach algebra and J be the Jacobson radical of A. (1) We firstly show that a is generalized Drazin invertible in A if and only if a+J is generalized Drazin invertible in A/J. Then we prove that a is pseudo Drazin invertible in A if and only if a+J is Drazin invertible in 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 A. We give the necessary and sufficient conditions under which elements in 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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