Non-stable subnormal contractions have nontrivial hyperinvariant subspaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915965558587392 |
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| author | Gamal', Maria F. |
| author_facet | Gamal', Maria F. |
| contents | A contraction $T$ on a (complex, separable) Hilbert space is stable, or of class $C_{0\cdot}$, if $T^n\to 0$ in the strong operator topology. It is proved that for a non-stable pure subnormal contraction $T$ there exists a singular inner function $θ$ such that the range of $θ(T)$ is not dense. Consequently, $T$ has nontrivial hyperinvariant subspaces. The proof is based on results by Esterle and Kérchy. Examples of stable subnormal contractions are given for which the range of $φ(T)$ is dense for every $φ\in H^\infty$ ($φ\not\equiv 0$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26044 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-stable subnormal contractions have nontrivial hyperinvariant subspaces Gamal', Maria F. Functional Analysis 47A15, 47A45, 47A60, 47B20 A contraction $T$ on a (complex, separable) Hilbert space is stable, or of class $C_{0\cdot}$, if $T^n\to 0$ in the strong operator topology. It is proved that for a non-stable pure subnormal contraction $T$ there exists a singular inner function $θ$ such that the range of $θ(T)$ is not dense. Consequently, $T$ has nontrivial hyperinvariant subspaces. The proof is based on results by Esterle and Kérchy. Examples of stable subnormal contractions are given for which the range of $φ(T)$ is dense for every $φ\in H^\infty$ ($φ\not\equiv 0$). |
| title | Non-stable subnormal contractions have nontrivial hyperinvariant subspaces |
| topic | Functional Analysis 47A15, 47A45, 47A60, 47B20 |
| url | https://arxiv.org/abs/2604.26044 |