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

Let be a Banach algebra. An element a ∈ has generalized Drazin inverse if there exists b ∈ such that b = bab, ab = ba, a - a2b ∈ 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...

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Bibliographic Details
Published inKyungpook mathematical journal Vol. 64; no. 2; pp. 205 - 218
Main Authors Farzaneh Tayebi, Nahid Ashrafi, Rahman Bahmani, Marjan Sheibani Abdolyousefi
Format Journal Article
LanguageKorean
Published 2024
Subjects
generalized Drazin inverse
operator matrix
spectral idempotent
additive property
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Summary:Let be a Banach algebra. An element a ∈ has generalized Drazin inverse if there exists b ∈ such that b = bab, ab = ba, a - a2b ∈ 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, Cvetković-Ilić and Wei from 2010.
Bibliography:KISTI1.1003/JNL.JAKO202421461827092
ISSN:1225-6951
0454-8124