Spectral constants for the quantum annulus
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917524280442880 |
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| author | Pal, Sourav Pascoe, James E. Tomar, Nitin |
| author_facet | Pal, Sourav Pascoe, James E. Tomar, Nitin |
| contents | We find several new estimates for the spectral constants $K(\mathbb A_r)$ for which a closed annulus $\overline{\mathbb A}_r$ or closed polyannulus $\overline{\mathbb A}^n_r$ is a $K$-spectral set for operators in the quantum annulus $\mathbb Q \mathbb A_r$. We give two alternative proofs to an existing estimate of spectral constant. The first proof capitalizes a dilation theorem due to McCullough and Pascoe, while the second proof involves a certain variety in the Euclidean biball. For commuting and doubly commuting operators in $\mathbb Q \mathbb A_r$, we find upper and lower bounds for the smallest spectral constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17560 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral constants for the quantum annulus Pal, Sourav Pascoe, James E. Tomar, Nitin Functional Analysis Complex Variables Operator Algebras We find several new estimates for the spectral constants $K(\mathbb A_r)$ for which a closed annulus $\overline{\mathbb A}_r$ or closed polyannulus $\overline{\mathbb A}^n_r$ is a $K$-spectral set for operators in the quantum annulus $\mathbb Q \mathbb A_r$. We give two alternative proofs to an existing estimate of spectral constant. The first proof capitalizes a dilation theorem due to McCullough and Pascoe, while the second proof involves a certain variety in the Euclidean biball. For commuting and doubly commuting operators in $\mathbb Q \mathbb A_r$, we find upper and lower bounds for the smallest spectral constants. |
| title | Spectral constants for the quantum annulus |
| topic | Functional Analysis Complex Variables Operator Algebras |
| url | https://arxiv.org/abs/2601.17560 |