Geodesic
Generalized Drazin invertibility of the sum of two elements in a Banach algebra
Filomat, Tome 36 (2022) no. 13, p. 4429

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DOI

In this paper, we study additive properties of the generalized Drazin inverse in a Banach algebra. We first show that a + b ∈ A d under the condition that a, b ∈ A d , aba π = λa π bab π a π , and then give some explicit expressions for the generalized Drazin inverse of the sum a + b under some weaker conditions than those used in the previous papers. Some known results are extended.
DOI : 10.2298/FIL2213429Q
Classification : 15A09, 16U80
Keywords: Banach algebra, generalized Drazin inverse, additive result 
Xiaolan Qin; Linzhang Lu. Generalized Drazin invertibility of the sum of two elements in a Banach algebra. Filomat, Tome 36 (2022) no. 13, p. 4429 . doi: 10.2298/FIL2213429Q
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     title = {Generalized {Drazin} invertibility of the sum of two elements in a {Banach} algebra},
     journal = {Filomat},
     pages = {4429 },
     year = {2022},
     volume = {36},
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     doi = {10.2298/FIL2213429Q},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2213429Q/}
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