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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |