Some converse problems on the g-Drazin invertibility in Banach algebras

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-04-09 DOI:10.1007/s43034-024-00344-x

Honglin Zou

引用次数: 0

Abstract

The main purpose of this paper is to investigate the converse problems of some well-known results related to the generalized Drazin (g-Drazin for short) inverse in Banach algebras. Let \({\mathcal {A}}\) be a Banach algebra and \(a,b\in {\mathcal {A}}\). First, we give the relationship between the Drazin (g-Drazin, group) invertibility of a, b and that of the sum \(a+b\) under certain conditions. Then, for a given polynomial \(f(x)\in {\mathbb {C}}[x]\), the g-Drazin invertibility of f(a), \(f(a^{d})\), f(ab), \(f(1-ab)\) and \(f(a+b)\) are investigated.

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关于巴拿赫代数中 g-Drazin 反演性的一些逆问题

本文的主要目的是研究与巴拿赫代数中广义德拉津（简称g-德拉津）逆相关的一些著名结果的逆问题。设 \({\mathcal {A}}\) 是一个巴拿赫代数，并且 \(a,b\in {\mathcal {A}}\) 是一个巴拿赫代数。首先，我们给出了在一定条件下，a, b 的 Drazin（g-Drazin，群）可逆性与和（a+b）可逆性之间的关系。然后，对于给定的多项式 \(f(x)\in {\mathbb} {C}}[x]\), 研究了 f(a)、\(f(a^{d})\)、f(ab)、\(f(1-ab)\)和\(f(a+b)\)的 g-Drazin 可逆性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.