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[1] Guo Li, Chen Jianlong, Zou Honglin, et al. Some additive results for the generalized Drazin inversein a Banach algebra [J]. Journal of Southeast University (English Edition), 2017, 33 (3): 382-386. [doi:10.3969/j.issn.1003-7985.2017.03.020]
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Some additive results for the generalized Drazin inversein a Banach algebra()
Banach代数中元素之和的广义Drazin逆的一些结果
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
33
Issue:
2017 3
Page:
382-386
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2017-09-30

Info

Title:
Some additive results for the generalized Drazin inversein a Banach algebra
Banach代数中元素之和的广义Drazin逆的一些结果
Author(s):
Guo Li1;  2;  Chen Jianlong1;  Zou Honglin1
1School of Mathematics, Southeast University, Nanjing 211189, China
2School of Mathematics and Statistics, Beihua University, Jilin 132013, China
郭丽1;  2;  陈建龙1;  邹红林1
1东南大学数学学院, 南京 211189; 2北华大学数学与统计学院, 吉林 132013
Keywords:
generalized Drazin inverse;  Banach algebra;  nilpotent element;  quasi-nilpotent element
广义Drazin逆;  Banach代数;  幂零元;  拟幂零元
PACS:
O151.21
DOI:
10.3969/j.issn.1003-7985.2017.03.020
Abstract:
Let a, b be two generalized Drazin invertible elements in a Banach algebra. An explicit expression for the generalized Drazin inverse of the sum a+b in terms of a, b, ad, bd is given. The generalized Drazin inverse for the sum of two elements in a Banach algebra is studied by means of the system of idempotents. It is first proved that a+b∈Aqnil under the condition that a, b∈Aqnil, aba=0 and ab2=0 and then the explicit expressions for the generalized Drazin inverse of the sum a+b under some new conditions are given. Also, some known results are extended.
令a, b为Banach代数中的2个广义Drazin可逆的元素.用a, b, ad, bd给出元素a+b和的广义Drazin逆的明确表达式.利用Banach代数中的幂等系统研究了2个元素之和的广义Drazin逆. 对于Banach代数中元素a, b, 首先证明了如果a, b∈Aqnil, aba=0且ab2=0, 则a+b∈Aqnil. 并在一些新的条件下给出了a+b和的广义Drazin逆的表达式, 推广了近期的一些结果.

References:

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Memo

Memo:
Biography: Guo Li(1980—), female, doctor, associate professor, guomingli95@163.com.
Foundation items: The National Natural Science Foundation of China(No.11371089, 11371165), the Natural Science Foundation of Jilin Province(No.20160101264JC), the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020), the Natural Science Foundation of Jiangsu Province(No.BK20141327), the Fundamental Research Funds for the Central Universities, the Foundation of Graduate Innovation Program of Jiangsu Province(No.KYZZ15-0049).
Citation: Guo Li, Chen Jianlong, Zou Honglin.Some additive results for the generalized Drazin inverse in a Banach algebra[J].Journal of Southeast University(English Edition), 2017, 33(3):382-386.DOI:10.3969/j.issn.1003-7985.2017.03.020.
Last Update: 2017-09-20