*-DMP elements in *-semigroups and *-rings

Chen

Linear and Multilinear Algebra

et al. 2021

Self Cite

A weak group element is introduced in a proper * -ring. Several equivalent conditions of weak group elements are investigated. We prove that an element is pseudo core invertible if it is both partial isometry and weak group invertible. Reverse order law and additive property of the weak group inverse are presented. Finally, under certain assumption on a, equivalent conditions of a W a * = a * a W are presented by using the normality of the group invertible part of an element in its group-EP decomposition.

Section: Preliminariesmentioning

confidence: 99%

Weak group inverses and partial isometries in proper *-rings

Chen

Linear and Multilinear Algebra

et al. 2021

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“…The notion of core-EP inverse for matrices was extended to elements of a ring with involution in [7] and generalized Drazin invertible operators on Hilbert space in [20]. For detailed results related to core-EP pre-orders, see [8,17,22].…”

Section: Introductionmentioning

confidence: 99%

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

Mosić¹

2019

J. Aust. Math. Soc.

We define extensions of the weighted core–EP inverse and weighted core–EP pre-orders of bounded linear operators on Hilbert spaces to elements of a $C^{\ast }$ -algebra. Some properties of the weighted core–EP inverse and weighted core–EP pre-orders are generalized and some new ones are proved. Using the weighted element, the weighted core–EP pre-order, the minus partial order and the star partial order of certain elements, new weighted pre-orders are presented on the set of all $wg$ -Drazin invertible elements of a $C^{\ast }$ -algebra. Applying these results, we introduce and characterize new partial orders which extend the core–EP pre-order to a partial order.

Linear and Multilinear Algebra

“…AA † is an orthogonal projector onto R(A k ) and A † A is an oblique projector on to R(A k ) along N ((A k ) † A). The core inverse and core-EP inverse have applications in partial order theory (see for example, [8][9][10]).…”

Section: Introductionmentioning

confidence: 99%

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

Gao

Chen

Patrício

2018

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In this paper, we investigate the weighted core-EP inverse introduced by Ferreyra, Levis and Thome. Several computational representations of the weighted core-EP inverse are obtained in terms of singular-value decomposition, full-rank decomposition and QR decomposition. These representations are expressed in terms of various matrix powers as well as matrix product involving the core-EP inverse, Moore-Penrose inverse and usual matrix inverse. Finally, those representations involving only Moore-Penrose inverse are compared and analyzed via computational complexity and numerical examples.