The G-Drazin Inverse of an Operator Matrix over Banach Spaces

Let A be a Banach algebra. An element a ∈ A has generalized Drazin inverse if there exists b ∈ A such that b = bab, ab = ba, a-a^2b ∈ A^(qnil). New additive results for the generalized Drazin inverse of an operator over a Banach space are presented. we extend the main results of a paper of Shakoor,...

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Published inKyungpook mathematical journal pp. 205 - 218
Main Authors Farzaneh Tayebi, Nahid Ashrafi, Rahman Bahmani, Marjan Sheibani Abdolyousefi
Format Journal Article
LanguageEnglish
Published 경북대학교 자연과학대학 수학과 01.06.2024
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수학
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Summary:Let A be a Banach algebra. An element a ∈ A has generalized Drazin inverse if there exists b ∈ A such that b = bab, ab = ba, a-a^2b ∈ A^(qnil). New additive results for the generalized Drazin inverse of an operator over a Banach space are presented. we extend the main results of a paper of Shakoor, Yang and Ali from 2013 and of Wang, Huang and Chen from 2017. Appling these results to 2×2 operator matrices we also generalize results of a paper of Deng, Cvetkovic-Ilic and Wei from 2010. KCI Citation Count: 0
ISSN:1225-6951
0454-8124
DOI:10.5666/KMJ.2024.64.2.205