Negative powers of Hilbert-space contractions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914713660555264 |
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| author | Ransford, Thomas |
| author_facet | Ransford, Thomas |
| contents | We show that, given a closed subset $E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence $u_n\to\infty$ with the following property: if $T$ is a Hilbert-space contraction such that $σ(T)\subset E$ and $\|T^{-n}\|=O(u_n)$ and rank$(I-T^*T)<\infty$, then $T$ is a unitary operator. We further show that the condition of measure zero is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10754 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Negative powers of Hilbert-space contractions Ransford, Thomas Functional Analysis Complex Variables Primary 30J15, 47A20, Secondary 47A30, 47A45, 47A56 We show that, given a closed subset $E$ of the unit circle of Lebesgue measure zero, there exists a positive sequence $u_n\to\infty$ with the following property: if $T$ is a Hilbert-space contraction such that $σ(T)\subset E$ and $\|T^{-n}\|=O(u_n)$ and rank$(I-T^*T)<\infty$, then $T$ is a unitary operator. We further show that the condition of measure zero is sharp. |
| title | Negative powers of Hilbert-space contractions |
| topic | Functional Analysis Complex Variables Primary 30J15, 47A20, Secondary 47A30, 47A45, 47A56 |
| url | https://arxiv.org/abs/2310.10754 |