Some relationships with subnormal operators and existence of hyperinvariant subspaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912574085267456 |
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| author | Gamal', Maria F. |
| author_facet | Gamal', Maria F. |
| contents | If $T$ is a polynomially bounded operator, $\mathcal M$ is an invariant subspace of $T$, $T|_{\mathcal M}$ is a unilateral shift and $T^*|_{\mathcal M^\perp}$ is subnormal, then $T$ has a nontrivial hyperinvariant subspace. If an operator $T$ is intertwined from both sides with two operators, one of which is hyponormal and other is the adjoint to hyponormal, then $T$ has a nontrivial hyperinvariant subspace. The existence of nontrivial hyperinvariant subspaces for subnormal operators themselves is not studied here. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some relationships with subnormal operators and existence of hyperinvariant subspaces Gamal', Maria F. Functional Analysis 47A15, 47B02, 47A60, 47B20 If $T$ is a polynomially bounded operator, $\mathcal M$ is an invariant subspace of $T$, $T|_{\mathcal M}$ is a unilateral shift and $T^*|_{\mathcal M^\perp}$ is subnormal, then $T$ has a nontrivial hyperinvariant subspace. If an operator $T$ is intertwined from both sides with two operators, one of which is hyponormal and other is the adjoint to hyponormal, then $T$ has a nontrivial hyperinvariant subspace. The existence of nontrivial hyperinvariant subspaces for subnormal operators themselves is not studied here. |
| title | Some relationships with subnormal operators and existence of hyperinvariant subspaces |
| topic | Functional Analysis 47A15, 47B02, 47A60, 47B20 |
| url | https://arxiv.org/abs/2509.05453 |