Additive property of pseudo Drazin inverse of elements in a Banach algebra

2013/07/27 by Huihui Zhu, Jianlong Chen, Zhu, Huihui +1
Computer Science · Mathematics · #15A09 #15A27 #16H99 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #math.RA #msc:15A09 #msc:15A27 #msc:16H99

paper · pdf · doi:10.48550/arxiv.1307.7232

arxiv created 2013/07/27 · openalex publication_date 2013/07/27 · arxiv updated 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study properties of pseudo Drazin inverse in a Banach algebra with unity 1. If ab=ba and a,b are pseudo Drazin invertible, we prove that a+b is pseudo Drazin invertible if and only if 1+a^‡b is pseudo Drazin invertible. Moreover, the formula of (a+b)^‡ is presented . When the commutative condition is weaken to ab=λba ~(λ≠ 0), we also show that a-b is pseudo Drazin invertible if and only if aa^‡(a-b)bb^‡ is pseudo Drazin invertible.

Citations

• Pseudo-Inverses in Associative Rings and Semigroups

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