On existence of hyperinvariant subspaces for quasinilpotent operators with a nonsymmetry in the growth of the resolvent
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911828851818496 |
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| author | Gamal', Maria F. |
| author_facet | Gamal', Maria F. |
| contents | Let $T$ be a quasinilpotent operator on a Banach space. Under assumptions of a certain nonsymmetry in the growth of the resolvent of $T$, it is proved that every operator in the commutant of $T$ is not unicellular. In particular, $T$ has nontrivial hyperinvariant subspaces. The proof is based on a modification of the reasoning of [S]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On existence of hyperinvariant subspaces for quasinilpotent operators with a nonsymmetry in the growth of the resolvent Gamal', Maria F. Functional Analysis 47A10, 47A15, 47B01 Let $T$ be a quasinilpotent operator on a Banach space. Under assumptions of a certain nonsymmetry in the growth of the resolvent of $T$, it is proved that every operator in the commutant of $T$ is not unicellular. In particular, $T$ has nontrivial hyperinvariant subspaces. The proof is based on a modification of the reasoning of [S]. |
| title | On existence of hyperinvariant subspaces for quasinilpotent operators with a nonsymmetry in the growth of the resolvent |
| topic | Functional Analysis 47A10, 47A15, 47B01 |
| url | https://arxiv.org/abs/2404.04348 |