Geodesic
Generalized Cline's formula for g-Drazin inverse in a ring
Filomat, Tome 35 (2021) no. 8, p. 2573

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DOI

In this paper, we give a generalized Cline's formula for the generalized Drazin inverse. Let R be a ring, and let a, b, c, d ∈ R satisfying (ac) 2 = (db)(ac), (db) 2 = (ac)(db); b(ac)a = b(db)a, c(ac)d = c(db)d. Then ac ∈ R d if and only if bd ∈ R d. In this case, (bd) d = b((ac) d) 2 d. We also present generalized Cline's formulas for Drazin and group inverses. Some weaker conditions in a Banach algebra are also investigated. These extend the main results of Cline's formula on g-Drazin inverse of Liao, Chen and Cui (Bull. Malays.). As an application, new common spectral property of bounded linear operators over Banach spaces is obtained
DOI : 10.2298/FIL2108573C
Classification : 15A09, 47A11
Keywords: Cline’s formula, Generalized Drazin inverse, Drazin inverse, group inverse, Banach algebra 
Huanyin Chen; Marjan Sheibani Abdolyousefi. Generalized Cline's formula for g-Drazin inverse in a ring. Filomat, Tome 35 (2021) no. 8, p. 2573 . doi: 10.2298/FIL2108573C
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     title = {Generalized {Cline's} formula for {g-Drazin} inverse in a ring},
     journal = {Filomat},
     pages = {2573 },
     year = {2021},
     volume = {35},
     number = {8},
     doi = {10.2298/FIL2108573C},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2108573C/}
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