Geodesic
Extension of the generalized n-strong Drazin inverse
Filomat, Tome 37 (2023) no. 23, p. 7781

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DOI

The aim of this paper is to present an extension of the generalized n-strong Drazin inverse for Banach algebra elements using a g–Drazin invertible element rather than a quasinilpotent element in the definition of the generalized n-strong Drazin inverse. Thus, we introduce a new class of generalized inverses which is a wider class than the classes of the generalized n-strong Drazin inverse and the extended generalized strong Drazin inverses. We prove a number of characterizations for this new inverse and some of them are based on idempotents and tripotents. Several generalizations of Cline's formula are investigated for the extension of the generalized n-strong Drazin inverse.
DOI : 10.2298/FIL2323781M
Classification : 46H05, 46H99, 15A09
Keywords: generalized n-strong Drazin inverse, extended g–Drazin inverse, g–Drazin inverse, Cline’s formula, Banach algebra 
Dijana Mosić; Honglin Zou; Long Wang. Extension of the generalized n-strong Drazin inverse. Filomat, Tome 37 (2023) no. 23, p. 7781 . doi: 10.2298/FIL2323781M
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     title = {Extension of the generalized n-strong {Drazin} inverse},
     journal = {Filomat},
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     year = {2023},
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     doi = {10.2298/FIL2323781M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2323781M/}
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