Tightening Bounds on the Numerical Radius for Hilbert Space Operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914095717941248 |
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| author | Jalili, Maryam Moradi, Hamid Reza |
| author_facet | Jalili, Maryam Moradi, Hamid Reza |
| contents | Let $S$ be a bounded linear operator on a Hilbert space. We show that if $S$ is accretive (resp. dissipative the sense that $\frac{S-{{S}^{*}}}{2i}$ is positive) in the sense that $\frac{S+{{S}^{*}}}{2}$ is positive, then \[\frac{\sqrt{3}}{3}\left\| S \right\|\le ω\left( S \right),\] where $\left\| \cdot \right\| $ and $ω\left( \cdot \right)$ denote the operator norm and the numerical radius, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tightening Bounds on the Numerical Radius for Hilbert Space Operators Jalili, Maryam Moradi, Hamid Reza Functional Analysis Operator Algebras Primary 47A12, Secondary 47A30, 47A63, 15A60 Let $S$ be a bounded linear operator on a Hilbert space. We show that if $S$ is accretive (resp. dissipative the sense that $\frac{S-{{S}^{*}}}{2i}$ is positive) in the sense that $\frac{S+{{S}^{*}}}{2}$ is positive, then \[\frac{\sqrt{3}}{3}\left\| S \right\|\le ω\left( S \right),\] where $\left\| \cdot \right\| $ and $ω\left( \cdot \right)$ denote the operator norm and the numerical radius, respectively. |
| title | Tightening Bounds on the Numerical Radius for Hilbert Space Operators |
| topic | Functional Analysis Operator Algebras Primary 47A12, Secondary 47A30, 47A63, 15A60 |
| url | https://arxiv.org/abs/2506.07226 |