Extension of the generalized n-strong Drazin inverse-Reference-Cited by-同舟云学术

Extension of the generalized n-strong Drazin inverse

Published:2023 Issue:23 Volume:37 Page:7781-7790
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Mosic Dijana¹^ORCID,Zou Honglin²,Wang Long³

Affiliation:

1. Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia

2. College of Basic Science, Zhejiang Shuren University, Hangzhou, China

3. School of Mathematical Sciences, Yangzhou University, Yangzhou, China

Abstract

The aim of this paper is to present an extension of the generalized n-strong Drazin inverse for Banach algebra elements using a g-Drazin invertible element rather than a quasinilpotent element in the definition of the generalized n-strong Drazin inverse. Thus, we introduce a new class of generalized inverses which is a wider class than the classes of the generalized n-strong Drazin inverse and the extended generalized strong Drazin inverses. We prove a number of characterizations for this new inverse and some of them are based on idempotents and tripotents. Several generalizations of Cline?s formula are investigated for the extension of the generalized n-strong Drazin inverse.

Publisher

National Library of Serbia

Reference22 articles.

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