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

被引：0
|
作者：
Chen, Huanyin [1 ]
Sheibani, Marjan [2 ]
机构：
[1] Fuzhou Univ Int Studies & Trade, Sch Big Data, Fuzhou 350202, Peoples R China
[2] Semnan Univ, Farzanegan Campus, Semnan, Iran
来源：
FILOMAT | 2024年 / 38卷 / 14期
关键词：
g-Drazin inverse; group inverse; block operator matrix; identical subblock; Banach space; REPRESENTATIONS; INVERTIBILITY;
D O I：
10.2298/FIL2414973C
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present the generalized Drazin inverse for certain anti-triangular operator matrices. Let E F , EF pi is an element of B ( X )( d) . If EFEF pi = 0 and F (2) EF pi = 0, we prove that M =(E (F) I (0) )has g-Drazin inverse and F 0 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 (pi) = 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 Mosic<acute accent> (Filomat, 32(2018), 5907-5917) and Zou, Chen and Mosic<acute accent> (Studia Scient. Math. Hungar., 54(2017), 489-508).
引用
收藏
页码：4973 / 4990
页数：18
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