We consider the generalized concept of order relations in Rickart rings and Rickart-rings
which was proposed by Šemrl and which covers the star partial order, the left-star partial …

Proper splittings of operators are commonly used to study the convergence of iterative
processes. In order to approximate solutions of operator equations, in this article we deal …

In this article we explore several aspects concerning to the Moore-Penrose inverse of a
bounded linear operator. On the one hand, we study monotonicity properties of the Moore …

Let B (H) be the algebra of all bounded linear operators on a complex Hilbert space H. In
1978, Drazin introduced a partial order,⩽∗, on B (H). For A, B∈ B (H), A⩽∗ B if and only if …

We give a simple necessary and sufficient condition for the existence of star supremum for
two arbitrary operators on a Hilbert space. It is shown that the results of Hartwig (1979)[15] …

Recently, in (Arias ML, Corach G, Maestripieri A. Range additivity, shorted operator and the
Sherman–Morrison–Woodburry formula, Linear Algebra Appl. 2015; 467), authors gave a …

We study the minus order on the algebra of bounded linear operators on a Hilbert space. By
giving a characterization in terms of range additivity, we show that the intrinsic nature of the …

In this paper, we establish some necessary and sufficient conditions for the existence of
solutions to the system of operator equations $ BXA= B= AXB $ in the setting of bounded …

Various authors have investigated properties of the star order (introduced by Drazin in 1978)
on algebras of matrices and of bounded linear operators on a Hilbert space. Rickart …

We study the star and minus partial orders on the set B (H, K) of all bounded operators
acting from a Hilbert space H to a Hilbert space K. We extend and strengthen some results …