Geodesic
Additive property for the generalized Zhou inverse in a Banach algebra
Filomat, Tome 37 (2023) no. 9, p. 2787

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Let A be a Banach algebra. An element a ∈ A has the generalized Zhou inverse if there exists b ∈ A such that b = bab, ab = ba, a n − ab ∈ J # (A), f or some n ∈ N. We find some new conditions under which the generalized Zhou inverse of the sum a + b can be explicitly expressed in terms of a, b, a z , b z. In particular, necessary and sufficient conditions for the existence of the generalized Zhou inverse of the sum a + b are obtained.
DOI : 10.2298/FIL2309787A
Classification : 15A09, 32A65, 16E50
Keywords: additive property, Banach algebra, generalized Zhou inverse 
Abbas Abbasi; Rahman Bahmani; Marjan Sheibani Abdolyousefi; Nahid Ashrafi. Additive property for the generalized Zhou inverse in a Banach algebra. Filomat, Tome 37 (2023) no. 9, p. 2787 . doi: 10.2298/FIL2309787A
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     author = {Abbas Abbasi and Rahman Bahmani and Marjan Sheibani Abdolyousefi and Nahid Ashrafi},
     title = {Additive property for the generalized {Zhou} inverse in a {Banach} algebra},
     journal = {Filomat},
     pages = {2787 },
     year = {2023},
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     number = {9},
     doi = {10.2298/FIL2309787A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2309787A/}
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