The Drazin inverse of the sum of two products
Commun. Korean Math. Soc. 2022 Vol. 37, No. 3, 705-718
Published online July 5, 2022
Printed July 31, 2022
Safae Alaoui~Chrifi, Abdelaziz Tajmouati
Sidi Mohamed Ben Abdellah University; Sidi Mohamed Ben Abdellah University
Abstract : In this paper, for bounded linear operators $A,B,C$ satisfying $[AB,B]=[BC,B]=[AB,BC]=0$ we study the Drazin invertibility of the sum of products formed by the three operators $A,B$ and $C$. In particular, we give an explicit representation of the anti-commutator $\{A,B\}=AB+BA$. Also we give some conditions for which the sum $A+C$ is Drazin invertible.
Keywords : Drazin inverse, additive results, bounded linear operator, operator matrix
MSC numbers : 15A09, 47A08, 47A55
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