G-Drazin inverse and group inverse for the anti-triangular block-operator matrices

2023/05/17 by Huanyin Chen, Chen, Huanyin, Marjan Sheibani +1
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2305.09951

openalex publication_date 2023/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present the generalized Drazin inverse for certain anti-triangular operator matrices. Let E,F,EF^π∈ B(X)^d. If EFEF^π=0 and F²EF^π=0, we prove that M=( E · amp;I F · amp;0 ) has g-Drazin inverse and its explicit representation is established. Moreover, necessary and sufficient conditions are given for the existence of the group inverse of M under the condition FEF^π=0. The group inverse for the anti-triangular block-operator matrices with two identical subblocks is thereby investigated. These extend the results of Zhang and Mosić (Filomat, 32(2018), 5907--5917) and Zou, Chen and Mosić (Studia Scient. Math. Hungar., 54(2017), 489--508).

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