# [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] 点击复制 关于Banach代数中伪Drazin逆的进一步结果() 分享到： var jiathis_config = { data_track_clickback: true };

47

2017年第3期

626-630

2017-05-20

## 文章信息/Info

Title:
Further results on pseudo Drazin inverse in Banach algebras

Author(s):
School of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

O151.2
DOI:
10.3969/j.issn.1001-0505.2017.03.034

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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