Weighted core–EP inverse of an operator between Hilbert spaces

Weighted Core–ep Inverse and Weighted Core–ep Pre-Orders in a -Algebra

“…Thus a d 3 = 0, which gives that a 3 is quasinilpotent. In the case where w ∈ A\{0} and a ∈ A is wg-Drazin invertible, we obtain new matrix representations of a and w, generalizing corresponding results for rectangular matrices in [6] and bounded linear operators between two Hilbert spaces in [18].…”

“…We now define and study the weighted core-EP inverse for an element of a C *algebra as an extension of the weighted core-EP inverse for a rectangular matrix [6] and bounded linear operator between Hilbert spaces [18] and the core-EP inverse for a square matrix [21] ,w wawA. Since a d,w waw is an idempotent, we have that a d,w wawA ∩ (a d,w waw) • = {0}.…”

“…Using a weighted element and the core-EP relation of certain elements, we introduce weighted core-EP binary relations on the set of all wg-Drazin invertible elements. Thus, we extend corresponding definitions of weighted core-EP pre-orders for bounded linear operators on Hilbert spaces [18] to elements of a C * -algebra.…”

“…As an extension of the core-EP inverse for a square matrix to a rectangular matrix, the weighted core-EP inverse was introduced in [6]. In [18], the weighted core-EP inverse of an operator between two Hilbert spaces was defined, generalizing the notion of the weighted core-EP inverse for a rectangular matrix. Also, using the core-EP preorder and minus partial order, the weighted core-EP pre-orders were presented on the set of all wg-Drazin invertible operators between two Hilbert spaces in [18].…”

Representations and properties of the W-weighted core-EP inverse

“…Then, Mosić [12] studied the weighted core-EP inverse of an operator between two Hilbert spaces as a generalization of the weighted core-EP inverse of a rectangular matrix. In this paper, our main goal is to further study the weighted core-EP inverse for a rectangular matrix and compile its new, computable representations.…”