Dijana Mosić

Reverse order law for the Moore-Penrose inverse in C*-algebras

In this paper we study several equivalent conditions related to the reverse order law for the Moore–Penrose inverse in C∗-algebras. We extend some well-known results to more general settings. Then we apply this result to obtain the reverse order rule for the weighted MoorePenrose inverse in C∗-algebras.

Partial isometries and EP elements in rings with involution

∗Received by the editors June 1, 2009. Accepted for publication November 12, 2009. Handling Editor: Michael J. Tsatsomeros. †Faculty of Sciences and Mathematics, University of Nǐs, P.O. Box 224, 18000 Nǐs, Serbia (sknme@ptt.rs, ganedj@eunet.rs). Supported by the Ministry of Science, Republic of Serbia, grant no. 144003. Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 18, pp. 761-772, December 2009

Representation for the generalized Drazin inverse of block matrices in Banach algebras

Abstract Several representations of the generalized Drazin inverse of a block matrix with a group invertible generalized Schur complement in Banach algebra are presented.

Reverse order law for the group inverse in rings

Abstract We investigate some necessary and sufficient conditions for the reverse order law for the group inverse in rings.

Weighted pre-orders involving the generalized Drazin inverse

The aim of this paper is to characterize new pre-orders defined on the set of all bounded linear operators between two Banach spaces. Thus, recent results on pre-orders involving the Drazin inverse of a complex matrix are extended to a more general setting.

Condition number of the W-weighted Drazin inverse

Abstract In this paper, we get the explicit condition number formulas for the W -weighted Drazin inverse of a rectangular matrix using the Schur decomposition and the spectral norm. We characterize the spectral norm and the Frobenius norm of the relative condition number of the W -weighted Drazin inverse, and the level-2 condition number of the W -weighted Drazin inverse. The sensitivity for the W -weighted Drazin inverse solution of linear systems is presented. We also present the structured perturbation of the W -weighted Drazin inverse.

Image-kernel (P,Q)-inverses in rings

UN-MONTIEL ‡ Abstract. Elements with equal idempotents related to their image-kernel (p,q)-inverses are characterized, and applications to perturbations, reverse order law and commutativity are given.

Further results on the reverse order law for the Moore–Penrose inverse in rings with involution

Abstract We present some equivalent conditions of the reverse order law for the Moore–Penrose inverse in rings with involution, extending some well-known results to more general settings. Then we apply this result to obtain a set of equivalent conditions to the reverse order rule for the weighted Moore–Penrose inverse in C ∗ -algebras.

Further results on partial isometries and EP elements in rings with involution

We investigate elements in rings with involution which are EP or partial isometries. Some well-known results are generalized.

Core-EP pre-order of Hilbert space operators

Abstract A new binary relation associated with the core–EP inverse is presented and studied on the corresponding subset of all generalized Drazin invertible bounded linear Hilbert space operators. Using the (dual) core partial order between core parts of operators and the minus partial order between quasinilpotent parts of operators, new pre-orders and partial orders are also introduced and characterized.