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

Qi Yang | Zendy; Xiaoji Liu | Zendy; Yaoming Yu | Zendy

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

Author(s) -

Qi Yang,

Xiaoji Liu,

Yaoming Yu

Publication year - 2021

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2021/6585951

Subject(s) - mathematics , moore–penrose pseudoinverse , order (exchange) , inverse , product (mathematics) , linear operators , pure mathematics , calculus (dental) , algebra over a field , mathematical analysis , geometry , medicine , dentistry , finance , economics , bounded function

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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