Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators
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 ABC†=C†B†A†. Moreover, several equivalent statements of ℛAA∗ABC=ℛABC...
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| Main Authors: | , , |
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| Format: | article |
| Language: | EN |
| Published: |
Hindawi Limited
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/7ecd1b2a961b480db7420aa7604fc1aa |
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| Summary: | 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 ABC†=C†B†A†. Moreover, several equivalent statements of ℛAA∗ABC=ℛABC and ℛC∗CABC∗=ℛABC∗ are also deducted by the theory of operators. |
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