On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=Q
In this paper, the positive operator solutions to operator equation X−A∗X−tA=Q (t > 1) are studied in infinite dimensional Hilbert space. Firstly, the range of norm and the spectral radius of the solution to the equation are given. Secondly, by constructing effective iterative sequence, it gives...
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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/10.1155/2021/7124859 |
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| _version_ | 1849415218548965376 |
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| author | Kaifan Yang |
| author_facet | Kaifan Yang |
| author_sort | Kaifan Yang |
| collection | DOAJ |
| description | In this paper, the positive operator solutions to operator equation X−A∗X−tA=Q (t > 1) are studied in infinite dimensional Hilbert space. Firstly, the range of norm and the spectral radius of the solution to the equation are given. Secondly, by constructing effective iterative sequence, it gives some conditions for the existence of positive operator solutions to operator equation X−A∗X−tA=Q (t > 1). The relations of these operators in the operator equation are given. |
| format | Article |
| id | doaj-art-5771912b8873440a893400e55fa476a0 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5771912b8873440a893400e55fa476a02025-08-20T03:33:35ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/71248597124859On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=QKaifan Yang0School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong, Shaanxi, ChinaIn this paper, the positive operator solutions to operator equation X−A∗X−tA=Q (t > 1) are studied in infinite dimensional Hilbert space. Firstly, the range of norm and the spectral radius of the solution to the equation are given. Secondly, by constructing effective iterative sequence, it gives some conditions for the existence of positive operator solutions to operator equation X−A∗X−tA=Q (t > 1). The relations of these operators in the operator equation are given.http://dx.doi.org/10.1155/2021/7124859 |
| spellingShingle | Kaifan Yang On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=Q Journal of Mathematics |
| title | On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=Q |
| title_full | On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=Q |
| title_fullStr | On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=Q |
| title_full_unstemmed | On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=Q |
| title_short | On the Positive Operator Solutions to an Operator Equation X−A∗X−tA=Q |
| title_sort | on the positive operator solutions to an operator equation x a∗x ta q |
| url | http://dx.doi.org/10.1155/2021/7124859 |
| work_keys_str_mv | AT kaifanyang onthepositiveoperatorsolutionstoanoperatorequationxaxtaq |