On the generalized Drazin inverse in Banach algebras in terms of the generalized Schur complement

On the generalized Drazin inverse in Banach algebras in terms of the generalized Schur complement

We present new results on existence and representation of the generalized Drazin inverse for elements in Banach algebras, involving the generalized Schur complement. They extend cases studied in the literature where the generalized Schur complement is assumed to be nonsingular, or zero, or group inv...

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Veröffentlicht in:Applied mathematics and computation 2016-07, Vol.284, p.162-168
Hauptverfasser: Robles, J., Martínez-Serrano, M.F., Dopazo, E.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Block matrix
Complement
Computation
Formulas (mathematics)
Generalized Drazin inverse
Generalized Schur complement
Inverse
Mathematical models
Representations
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Beschreibung
Zusammenfassung:We present new results on existence and representation of the generalized Drazin inverse for elements in Banach algebras, involving the generalized Schur complement. They extend cases studied in the literature where the generalized Schur complement is assumed to be nonsingular, or zero, or group invertible. The results are applied to obtain formulas for cases of special interest.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2016.02.057