2023/02/13 by Honglin Zou, Tingting Li, Zou, Honglin +3
Computer Science · Engineering · Mathematics · #15A09 #32A65 #47A10 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2302.06080
openalex publication_date 2023/02/13 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
In a Banach algebra, we introduce a new type of generalized inverse called gπ-Hirano inverse. Firstly, several existence criteria and the equivalent definition of this inverse are investigated. Then, we discuss the relationship between the gπ-Hirano invertibility of a, b and that of the sum a+b under some weaker conditions. Finally, as applications to the previous additive results, some equivalent characterizations for the gπ-Hirano invertibility of the anti-triangular matrix over Banach algebras are obtained.In particular, some results in this paper are different from the corresponding ones of classical generalized inverses, such as Drazin inverse and generalized Drazin inverse.