[1]邹红林,陈建龙.关于Banach代数中伪Drazin逆的进一步结果[J].东南大学学报(自然科学版),2017,47(3):626-630.[doi:10.3969/j.issn.1001-0505.2017.03.034]
　Zou Honglin,Chen Jianlong.Further results on pseudo Drazin inverse in Banach algebras[J].Journal of Southeast University (Natural Science Edition),2017,47(3):626-630.[doi:10.3969/j.issn.1001-0505.2017.03.034]
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关于Banach代数中伪Drazin逆的进一步结果()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
47
期数:
2017年第3期
页码:
626-630
栏目:
数学、物理学、力学
出版日期:
2017-05-20

文章信息/Info

Title:
Further results on pseudo Drazin inverse in Banach algebras
作者:
邹红林; 陈建龙
东南大学数学学院, 南京 210096
Author(s):
Zou Honglin;  Chen Jianlong
School of Mathematics, Southeast University, Nanjing 210096, China
关键词:
伪Drazin逆;  Jacobson根;  Banach代数
Keywords:
pseudo Drazin inverse;  Jacobson radical;  Banach algebra
分类号:
O151.2
DOI:
10.3969/j.issn.1001-0505.2017.03.034
摘要:
在条件ab=φ(ba)下,研究了ab与a+b的伪Drazin逆的表达式. 其中, a,b是Banach代数A中的2个伪Drazin可逆的元素,φ是A上双射的centralizer.证明了:若a,b是伪Drazin可逆的且ab=φ(ba), 则ab是伪Drazin可逆的且(ab)?=b?a?; a+b是伪Drazin可逆的,当且仅当aa?(a+b)是伪Drazin可逆的,当且仅当aa?(a+b)bb?是伪Drazin可逆的. 此时,(a+b)?=(aa?(a+b))?+∑∞n=0φ-(n(n+1))/2(0121)(b?)n+1(-a)n(11-aa?).
Abstract:
Let a,b be two pseudo Drazin invertible elements in a Banach algebra A. The expressions of the pseudo Drazin inverse of ab and a+b are studied under the condition ab=φ(ba), where φ is a bijective centralizer on A. It is proved that if a,b∈A are pseudo Drazin invertible and ab=φ(ba), then ab is pseudo Drazin invertible with (ab)?=b?a?; a+b is pseudo Drazin invertible if and only if aa?(a+b) is pseudo Drazin invertible if and only if aa?(a+b)bb? is pseudo Drazin invertible. In this case, (a+b)?=(aa?(a+b))?+∑∞n=0φ-(n(n+1))/2(0121)(b?)n+1(-a)n(11-aa?).

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2016-09-01.
作者简介: 邹红林(1982─), 男, 博士生; 陈建龙(联系人), 男, 博士, 教授, 博士生导师,jlchen@seu.edu.cn.
基金项目: 国家自然科学基金资助项目(11371089)、江苏省普通高校研究生科研创新计划资助项目(KYZZ15-0049)、 江苏省自然科学基金资助项目(BK20141327).
引用本文: 邹红林,陈建龙.关于Banach代数中伪Drazin逆的进一步结果[J].东南大学学报(自然科学版),2017,47(3):626-630. DOI:10.3969/j.issn.1001-0505.2017.03.034.
更新日期/Last Update: 2017-05-20