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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6585951 |
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| author | Yang Qi Liu Xiaoji Yu Yaoming |
| author_facet | Yang Qi Liu Xiaoji Yu Yaoming |
| author_sort | Yang Qi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7ecd1b2a961b480db7420aa7604fc1aa |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7ecd1b2a961b480db7420aa7604fc1aa2025-02-03T05:49:26ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/6585951Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear OperatorsYang Qi0Liu Xiaoji1Yu Yaoming2College of Mathematics and Computing ScienceCollege of Mathematics and Computing ScienceCollege of EducationIn 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.http://dx.doi.org/10.1155/2021/6585951 |
| spellingShingle | Yang Qi Liu Xiaoji Yu Yaoming Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators Journal of Mathematics |
| title | Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators |
| title_full | Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators |
| title_fullStr | Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators |
| title_full_unstemmed | Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators |
| title_short | Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators |
| title_sort | developing reverse order law for the moore penrose inverse with the product of three linear operators |
| url | http://dx.doi.org/10.1155/2021/6585951 |
| work_keys_str_mv | AT yangqi developingreverseorderlawforthemoorepenroseinversewiththeproductofthreelinearoperators AT liuxiaoji developingreverseorderlawforthemoorepenroseinversewiththeproductofthreelinearoperators AT yuyaoming developingreverseorderlawforthemoorepenroseinversewiththeproductofthreelinearoperators |