$q$-Numerical Ranges and Spectral Sets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915867401388032 |
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| author | O'Loughlin, Ryan Rani, Jyoti |
| author_facet | O'Loughlin, Ryan Rani, Jyoti |
| contents | We study spectral constants for convex domains $Ω$ containing the spectrum of an operator. We extend the Crouzeix--Palencia framework by obtaining bounds depending on a parameter $γ$ and relating these bounds to geometric properties of $Ω$ and the numerical range $W(A)$. We generalise the proof that the numerical range is a $1+\sqrt{2}$-spectral set to scaled $q$-numerical ranges. We also propose a generalisation of Crouzeix's Conjecture in the context of $q$-numerical ranges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15536 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $q$-Numerical Ranges and Spectral Sets O'Loughlin, Ryan Rani, Jyoti Functional Analysis 47A12, 47A25, 47A60 We study spectral constants for convex domains $Ω$ containing the spectrum of an operator. We extend the Crouzeix--Palencia framework by obtaining bounds depending on a parameter $γ$ and relating these bounds to geometric properties of $Ω$ and the numerical range $W(A)$. We generalise the proof that the numerical range is a $1+\sqrt{2}$-spectral set to scaled $q$-numerical ranges. We also propose a generalisation of Crouzeix's Conjecture in the context of $q$-numerical ranges. |
| title | $q$-Numerical Ranges and Spectral Sets |
| topic | Functional Analysis 47A12, 47A25, 47A60 |
| url | https://arxiv.org/abs/2603.15536 |