scholarly journals Hartwig’s triple reverse order law in C*-algebras

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4229-4232
Author(s):  
Jovana Milosevic
Keyword(s):  
Hilbert Spaces ◽  
Reverse Order ◽  
Algebraic Proof ◽  
C Algebras ◽  
Reverse Order Law

In this paper Hartwig?s triple reverse order law for the Moore-Penrose inverse is proved for C*-algebras. A very simple algebraic proof for Hartwig?s triple reverse order law for operators on Hilbert spaces is given.

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.

Reverse order law in C∗-algebras

2011 ◽  
Vol 218 (7) ◽  
pp. 3934-3941 ◽  
Author(s):  
Dijana Mosić ◽  
Dragan S. Djordjević
Keyword(s):  
Reverse Order ◽  
C Algebras ◽  
Reverse Order Law

scholarly journals Algebraic proof methods for identities of matrices and operators: Improvements of Hartwig’s triple reverse order law

2021 ◽  
Vol 409 ◽  
pp. 126357
Author(s):  
Dragana S. Cvetković-Ilić ◽  
Clemens Hofstadler ◽  
Jamal Hossein Poor ◽  
Jovana Milošević ◽  
Clemens G. Raab ◽  
...  
Keyword(s):  
Reverse Order ◽  
Algebraic Proof ◽  
Reverse Order Law ◽  
Proof Methods

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.

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