[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()

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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

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

Keywords:

generalized Drazin inverse;  Banach algebra;  nilpotent element;  quasi-nilpotent element

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, a^d, b^d 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∈A^qnil under the condition that a, b∈A^qnil, 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.

References:

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[13] Zou H L, Mosi D, Chen J L. Generalized Drazin invertibility of product and sum of two elements in a Banach algebra and its applications [J]. Turkish Journal of Mathematics, 2017, 41:548-563. Doi:10.3906/mat-1605-8.
[14] Benítez J, Liu X J, Qin Y H. Representations for the generalized Drazin inverse in a Banach algebra [J]. Bulletin of Mathematical Analysis and Applications, 2013, 5(1): 53-64.
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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.

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