Similarity of C1: Operators and the Hyperinvariant Subspace Problem
In the present paper, we first show that the existence of the solutions of the operator equation S∗XT=X is related to the similarity of operators of class C1., and then we give a sufficient condition for the existence of nontrivial hyperinvariant subspaces. These subspaces are the closure of ranφT f...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/9943902 |
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| _version_ | 1832559678212538368 |
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| author | Abdelkader Segres Ahmed Bachir Sid Ahmed Ould Ahmed Mahmoud |
| author_facet | Abdelkader Segres Ahmed Bachir Sid Ahmed Ould Ahmed Mahmoud |
| author_sort | Abdelkader Segres |
| collection | DOAJ |
| description | In the present paper, we first show that the existence of the solutions of the operator equation S∗XT=X is related to the similarity of operators of class C1., and then we give a sufficient condition for the existence of nontrivial hyperinvariant subspaces. These subspaces are the closure of ranφT for some singular inner functions φ. As an application, we prove that every C10-quasinormal operator and C10-centered operator, under suitable conditions, have nontrivial hyperinvariant subspaces. |
| format | Article |
| id | doaj-art-250b4623074548a48289a9e320e1958f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-250b4623074548a48289a9e320e1958f2025-02-03T01:29:25ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/9943902Similarity of C1: Operators and the Hyperinvariant Subspace ProblemAbdelkader Segres0Ahmed Bachir1Sid Ahmed Ould Ahmed Mahmoud2Department of MathematicsDepartment of MathematicsDepartment of MathematicsIn the present paper, we first show that the existence of the solutions of the operator equation S∗XT=X is related to the similarity of operators of class C1., and then we give a sufficient condition for the existence of nontrivial hyperinvariant subspaces. These subspaces are the closure of ranφT for some singular inner functions φ. As an application, we prove that every C10-quasinormal operator and C10-centered operator, under suitable conditions, have nontrivial hyperinvariant subspaces.http://dx.doi.org/10.1155/2024/9943902 |
| spellingShingle | Abdelkader Segres Ahmed Bachir Sid Ahmed Ould Ahmed Mahmoud Similarity of C1: Operators and the Hyperinvariant Subspace Problem Journal of Mathematics |
| title | Similarity of C1: Operators and the Hyperinvariant Subspace Problem |
| title_full | Similarity of C1: Operators and the Hyperinvariant Subspace Problem |
| title_fullStr | Similarity of C1: Operators and the Hyperinvariant Subspace Problem |
| title_full_unstemmed | Similarity of C1: Operators and the Hyperinvariant Subspace Problem |
| title_short | Similarity of C1: Operators and the Hyperinvariant Subspace Problem |
| title_sort | similarity of c1 operators and the hyperinvariant subspace problem |
| url | http://dx.doi.org/10.1155/2024/9943902 |
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