Hirano inverse of anti-triangular matrix over Banach Algebras

2023/03/27 by Gou, Haibo, Chen, Huanyin
#15A09 #16U99 #47A08 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2303.15146

Abstract

In this paper we investigate Hirano invertibility of anti-triangular matrix over a Banach algebra. Let a∈ \mathcal A^H, b∈ \mathcal A^sD. If b^Da=0, bab^π=0, we prove that \beginpmatrix a&1 b&0 \endpmatrix∈ M₂(\mathcal A)^H. Moreover, we considered Hirano invertibility of anti-triangular matrices under commutative-like conditions. These provide new kind of operator matrices with tripotent and nilpotent decompositions.

Related

• On the gπ-Hirano invertibility in Banach algebras
• Study on Hirano Invertibility of Two New Types of Perturbed Operator Matrices
• The g-Drazin invertibility in a Banach algebra
• Generalized Hirano inverses in Banach Algebra
• New characterizations of G-Drazin inverse in Banach algebra