Some remarks on possible generalized inverses in semigroups.
Kečkić, Jovan (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Kečkić, Jovan (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Tian, Yong-ge (2002)
Applied Mathematics E-Notes [electronic only]
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Kečkić, Jovan D., Milić, Svetozar (1999)
Publications de l'Institut Mathématique. Nouvelle Série
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Vladimiro Valerio (1981)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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Kalogeropoulos, Grigoris I., Karageorgos, Athanasios D., Pantelous, Athanasios A. (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Rakočević, Vladimir (1997)
Matematichki Vesnik
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M. Haverić (1984)
Matematički Vesnik
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Meenakshi, Ar., Anandam, N. (1992)
International Journal of Mathematics and Mathematical Sciences
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Gan, Gaoxiong (2002)
International Journal of Mathematics and Mathematical Sciences
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Jovan D. Kečkić (1989)
Publications de l'Institut Mathématique
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Dragan S. Djordjević, Stanimirović, Predrag S. (2001)
Czechoslovak Mathematical Journal
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We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range...
Pedro Patrício, António Costa (2009)
Open Mathematics
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It is known that the existence of the group inverse a # of a ring element a is equivalent to the invertibility of a 2 a − + 1 − aa −, independently of the choice of the von Neumann inverse a − of a. In this paper, we relate the Drazin index of a to the Drazin index of a 2 a − + 1 − aa −. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.