Some Results on the Symmetric Representation of the Generalized Drazin Inverse in a Banach Algebra

被引：3

作者：

Qin, Yonghui ^{[1
]}

Liu, Xiaoji ^{[2
]}

Benitez, Julio ^{[3
]}

机构：

[1] Guilin Univ Elect Technol, Coll Math & Comp Sci, Guilin 541004, Peoples R China

[2] Guangxi Univ Nationalities, Coll Math & Comp Sci, Nanning 530006, Peoples R China

[3] Univ Politecn Valencia, Dept Appl Math, E-46022 Valencia, Spain

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 01期

基金：

中国国家自然科学基金;

关键词：

generalized Drazin inverse; Banach algebra; representation; SUM;

D O I：

10.3390/sym11010105

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Based on the conditions ab(2) = 0 and b pi(ab) is an element of A(d), we derive that (ab)(n), (ba)(n), and ab + ba are all generalized Drazin invertible in a Banach algebra A, where n is an element of N and a and b are elements of A. By using these results, some results on the symmetry representations for the generalized Drazin inverse of ab + ba are given. We also consider that additive properties for the generalized Drazin inverse of the sum a + b.

引用

页数：9

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