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.
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页数：9
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