Geodesic
An extension of Hirano inverses in Banach algebras
Filomat, Tome 36 (2022) no. 9, p. 3197

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DOI

We introduce a new class of generalized inverse which is called π−Hirano inverse. In this paper some elementary properties of the π−Hirano inverse are obtained. We prove that a ∈ A is π−Hirano invertible if and only if a − a n+1 is nilpotent for some positive integer n. Certain multiplicative and additive results for the π−Hirano inverse in a Banach algebra are presented. We then apply these new results to block operator matrices over Banach spaces.
DOI : 10.2298/FIL2209197G
Classification : 15A09, 32A65, 16E50
Keywords: Drazin inverse, π−Hirano inverse, additive property, operator matrix, perturbation 
Ali Ghaffari; Tahere Haddadi; Marjan Sheibani Abdolyousefi. An extension of Hirano inverses in Banach algebras. Filomat, Tome 36 (2022) no. 9, p. 3197 . doi: 10.2298/FIL2209197G
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     title = {An extension of {Hirano} inverses in {Banach} algebras},
     journal = {Filomat},
     pages = {3197 },
     year = {2022},
     volume = {36},
     number = {9},
     doi = {10.2298/FIL2209197G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2209197G/}
}
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