Commun. Korean Math. Soc. 2022; 37(3): 705-718
Online first article July 5, 2022 Printed July 31, 2022
https://doi.org/10.4134/CKMS.c210040
Copyright © The Korean Mathematical Society.
Safae Alaoui~Chrifi, Abdelaziz Tajmouati
Sidi Mohamed Ben Abdellah University; Sidi Mohamed Ben Abdellah University
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
2004; 19(4): 715-720
2010; 25(4): 547-556
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