In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings. Moreover, if the ring has an involution, we present more equivalences when both involved elements are EP.

Abstract The aim of this work is to extend bounded finite potent endomorphisms on arbitrary Hilbert spaces the notions Drazin-Star and Star-Drazin matrices that have been recently introduced by D. Mosi?. existence, structure main properties these operators are given. In particular, we obtain new a complex matrix. Moreover, explicit solutions some infinite linear systems from inverse endomorphis...

The purpose of this paper is to investigate solvability systems constrained matrix equations in the form minimization problems. main novelty unification solutions considered with corresponding For a particular case we extend some well-known results and give several new for weak Drazin inverse. characterizations inverse, group inverse Moore–Penrose are obtained as consequences.

In this paper, we prove that the class of all generalized Drazin-Riesz invertible operators forms a regularity.

We present an extension, for Banach algebras, of the due to Corach et al, Jacobson’s lemma on g-Drazin inverse (Comm. Algebra, 41(2013), 520–531).

In this paper, we investigate the Sherman-Morrison-Woodbury formula for {1}-inverses and {2}-inverses of bounded linear operators on a Hilbert space. Some conditions are established to guarantee that (A+YGZ*)? = A? ?A?Y(G? +Z*A?Y)?Z*A? holds, where stands any kind standard inverse, {1}-inverse, {2}-inverse, Moore-Penrose Drazin group core inverse dual A.

In this paper we generalize the concept of Koliha-Drazin invertible operators by introducing generalized Drazin-1-meromorphic operators. A bounded linear operator T on a Banach space X is said to be 1-meromorphic if every non-zero point its spectrum an isolated point. For say that it there exists S acting such TS = ST, STS S, TST ? 1-meromorphic, while admits Kato-1-meromorphic decomposition pa...