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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.01201 |
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| _version_ | 1866912801544470528 |
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| author | Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. |
| author_facet | Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. |
| contents | We consider Cesáro operator on the Hardy space $H^p(\mathbb{C}_+)$ in the upper half-plane for $1<p<\infty$. In \cite{AS} it was proved that for all $1<p<\infty$ the spectrum of the operator $V=\frac{2(p-1)}{p}C-I$ is located on the unit circle and in \cite{ABC1} the authors of this note showed that for $p=2$ operator $V$ is unitary. In the present note we show that for $1<p<\infty$, $p\ne 2$, the norm of the operator $V$ is strictly greater than one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Remark Concerning Cesáro Operator on the Hardy Space $H^p(\mathbb{C}_+)$ in the Upper Half-Plane Andreev, Valentin V. Bekker, Miron B. Cima, Joseph A. Functional Analysis 47B38, 30H10, 47B32 We consider Cesáro operator on the Hardy space $H^p(\mathbb{C}_+)$ in the upper half-plane for $1<p<\infty$. In \cite{AS} it was proved that for all $1<p<\infty$ the spectrum of the operator $V=\frac{2(p-1)}{p}C-I$ is located on the unit circle and in \cite{ABC1} the authors of this note showed that for $p=2$ operator $V$ is unitary. In the present note we show that for $1<p<\infty$, $p\ne 2$, the norm of the operator $V$ is strictly greater than one. |
| title | Remark Concerning Cesáro Operator on the Hardy Space $H^p(\mathbb{C}_+)$ in the Upper Half-Plane |
| topic | Functional Analysis 47B38, 30H10, 47B32 |
| url | https://arxiv.org/abs/2601.01201 |