The g-Drazin inverses of anti-triangular block operator matrices

2022/09/28 by Huanyin Chen, Chen, Huanyin, Marjan Sheibani +1
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2209.13835

Abstract

An element a in a Banach algebra A has g-Drazin inverse if there exists b∈ A such that ab=ba, b=bab and a-a²b ∈ A^qnil. In this paper we find new explicit representations of the g-Drazin inverse of the block operator matrix ( E · amp;I F · amp;0 ). We thereby solve a wider kind of singular differential equations posed by Campbell [S.L. Campbell, The Drazin inverse and systems of second order linear differential equations, Linear & Multilinear Algebra, 14(1983), 195--198].

Related

• Representation of the g-Drazin inverse in a Banach algebra
• New characterizations of G-Drazin inverse in Banach algebra
• The g-Drazin invertibility in a Banach algebra
• Expressions for the g-Drazin inverse in a Banach algebra
• G-Drazin inverse and group inverse for the anti-triangular block-operator matrices