scholarly journals Reverse order law (ab)+ = b+(a+abb+)+a+ in rings with involution

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1791-1815 ◽  
Author(s):  
Dijana Mosic ◽  
Nebojsa Dincic
Keyword(s):  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution ◽  
Equivalent Conditions

In this paperwestudy several equivalent conditions for the reverse order law (ab)+ = b+(a+abb+)+a+ in rings with involution. We extend some well-known results to more general settings.

On the group invertibility of operators

2016 ◽  
Vol 31 ◽  
pp. 492-510
Author(s):  
Chunyuan Deng
Keyword(s):  
Hilbert Spaces ◽  
Main Topic ◽  
Reverse Order ◽  
Operator Matrices ◽  
Reverse Order Law ◽  
Block Operator ◽  
Block Operator Matrices ◽  
Group Inverses ◽  
Triangular Block ◽  
Equivalent Conditions

The main topic of this paper is the group invertibility of operators in Hilbert spaces. Conditions for the existence of the group inverses of products of two operators and the group invertibility of anti-triangular block operator matrices are studied. The equivalent conditions related to the reverse order law for the group inverses of operators are obtained.

Weighted Reverse Order Law for the Weighted Moore-Penrose Inverse in Rings with Involution

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution ◽  
Necessary And Sufficient

Abstract We investigate some necessary and sufficient conditions for the reverse order law for the weighted Moore-Penrose inverse in rings with involution.

scholarly journals Core partial order in rings with involution

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5695-5701 ◽  
Author(s):  
Xiaoxiang Zhang ◽  
Sanzhang Xu ◽  
Jianlong Chen
Keyword(s):  
Partial Order ◽  
Partial Orders ◽  
Reverse Order ◽  
Unital Ring ◽  
Reverse Order Law ◽  
Rings With Involution ◽  
Invertible Elements

Let R be a unital ring with involution. Several characterizations and properties of core partial order in R are given. In particular, we investigate the reverse order law (ab)# = b#a# for two core invertible elements a, b ? R. Some relationships between core partial order and other partial orders are obtained.

Mixed-type reverse order laws for the group inverses in rings with involution

2016 ◽  
Vol 53 (2) ◽  
pp. 138-156
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Mixed Type ◽  
Reverse Order ◽  
Rings With Involution ◽  
Group Inverses ◽  
Equivalent Conditions

We investigate some equivalent conditions for the reverse order laws (ab)# = b†a# and (ab)# = b#a† in rings with involution. Similar results for (ab)# = b#a* and (ab)# = b*a# are presented too.

Some results on the reverse order law in rings with involution

2012 ◽  
Vol 83 (3) ◽  
pp. 271-282 ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution

scholarly journals Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yang Qi ◽  
Liu Xiaoji ◽  
Yu Yaoming
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Reverse Order ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Reverse Order Law ◽  
Equivalent Conditions

In this paper, we study the reverse order law for the Moore–Penrose inverse of the product of three bounded linear operators in Hilbert spaces. We first present some equivalent conditions for the existence of the reverse order law A B C † = C † B † A † . Moreover, several equivalent statements of ℛ A A ∗ A B C = ℛ A B C and ℛ C ∗ C A B C ∗ = ℛ A B C ∗ are also deducted by the theory of operators.

scholarly journals Mixed-type reverse order law for Moore-Penrose inverse of products of three elements in ring with involution

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 1997-2008 ◽  
Author(s):  
Long Wang ◽  
Shuang Zhang ◽  
Xiao Zhang ◽  
Jian Chen
Keyword(s):  
Mixed Type ◽  
Reverse Order ◽  
Reverse Order Law ◽  
Rings With Involution

In this paper we establish some results concerning the mixed-type reverse order laws for the Moore-Penrose inverse of various products of three elements in rings with involution.

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