Communications of the
Korean Mathematical Society CKMS

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