Generalized Drazin invertibility of combinations of idempotents
JJ Koliha, Dragana Cvetkovic-Ilic, Chunyuan Deng
LINEAR ALGEBRA AND ITS APPLICATIONS | ELSEVIER SCIENCE INC | Published : 2012
The paper serves as a correction to J. Math. Anal. Appl. 359 (2009) 731-738 dealing with the Drazin invertibility of combinations of idempotents p,q in a Banach algebra. As the arguments employed to do this work equally well for both the usual and generalized Drazin inverse, the latter is included in the discussion which covers the equivalence of the Drazin invertibility of 1-pq, p-q, p+q and in general of αp+βq with αβ≠0, as well as the equivalence of the Drazin invertibility of the commutator pq-qp and anticommutator pq+qp of p,q. © 2012 Elsevier Inc. All rights reserved.